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AP Calculus AB Flashcards: Derivative Rules Of Constant Sum Difference

Study Derivative Rules Of Constant Sum Difference in AP Calculus AB with focused flashcards that help you recognize the idea, recall the key rule, and apply it in practice-style prompts.

← Back to flashcard decks

What this deck covers

This deck focuses on Derivative Rules Of Constant Sum Difference, giving you a quick way to review the definitions, rules, and examples that matter most for AP Calculus AB.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

AP Calculus AB Flashcards: Derivative Rules Of Constant Sum Difference

/ 30

0 reviewed

0% Complete

0 reviewing

QUESTION

Given $f(x) = x^2 + 3x$ , find $f'(x)$ .

Tap or drag to reveal answer

ANSWER

2x + 3. Apply power rule to each term separately.

Swipe Right = I Know It! 🎉

Swipe Left = Still Learning

All flashcards

Flashcard 1: Given $f(x) = x^2 + 3x$ , find $f'(x)$ .

Answer: 2x + 3. Apply power rule to each term separately.

Flashcard 2: What is the derivative of a constant $c$ with respect to $x$ ?

Answer:

Constants have zero rate of change.

Flashcard 3: Calculate the derivative of $7x^3 - 4x$ .

Answer: 21x^2 - 4. Use power rule: $7 \cdot 3x^2 - 4 = 21x^2 - 4$ .

Flashcard 4: State the derivative of the function $-5$ .

Answer:

Any constant has derivative zero.

Flashcard 5: Calculate the derivative of $12x$ .

Answer:

Derivative of linear term $12x$ is the coefficient.

Flashcard 6: What is the derivative of a constant multiplied by $x$ , $7x$ ?

Answer:

Constant multiple rule: derivative of $cx$ is $c$ .

Flashcard 7: Find the derivative of $8x - 2$ .

Answer:

Derivative of linear term is its coefficient.

Flashcard 8: State the derivative of $x^n$ where $n$ is a constant.

Answer: $nx^{n-1}$ . Power rule: bring down exponent, reduce by 1.

Flashcard 9: Given $f(x) = x^2 + 3x$ , find $f'(x)$ .

Answer: 2x + 3. Apply power rule to each term separately.

Flashcard 10: What is the derivative of $cf(x)$ , where $c$ is a constant?

Answer: $(cf)' = cf'$ . Constant multiple rule: factor out the constant.

Flashcard 11: State the derivative rule for the difference of two functions $f(x)$ and $g(x)$ .

Answer: $(f - g)' = f' - g'$ . Derivative of difference equals difference of derivatives.

Flashcard 12: What is the derivative of a constant $c$ with respect to $x$ ?

Answer:

Constants have zero rate of change.

Flashcard 13: Calculate the derivative of $5x - 3$ .

Answer:

Derivative of linear function is the coefficient of $x$ .

Flashcard 14: State the derivative rule for the sum of two functions $f(x)$ and $g(x)$ .

Answer: $(f + g)' = f' + g'$ . Derivative of sum equals sum of derivatives.

Flashcard 15: Calculate the derivative of $7x^3 - 4x$ .

Answer: 21x^2 - 4. Use power rule: $7 \cdot 3x^2 - 4 = 21x^2 - 4$ .

Flashcard 16: Find the derivative of $8x - 2$ .

Answer:

Derivative of linear term is its coefficient.

Flashcard 17: What is $rac{d}{dx}[2f(x)+3g(x)-5]$ ?

Answer: $2f'(x)+3g'(x)$ . Constant -5 has derivative 0; apply rules to rest.

Flashcard 18: What is $rac{d}{dx}[f(x)-g(x)+h(x)]$ ?

Answer: $f'(x)-g'(x)+h'(x)$ . Apply sum/difference rules term by term.

Flashcard 19: What is $rac{d}{dx}[f(x)+g(x)+h(x)]$ ?

Answer: $f'(x)+g'(x)+h'(x)$ . Sum rule extends to any number of functions.

Flashcard 20: What is $rac{d}{dx}[12-g(x)]$ ?

Answer: $-g'(x)$ . Derivative of 12 is 0; $-g(x)$ gives $-g'(x)$ .

Flashcard 21: What is $rac{d}{dx}[f(x)+9]$ ?

Answer: $f'(x)$ . Derivative of constant 9 is 0, leaving $f'(x)$ .

Flashcard 22: What is $rac{d}{dx}[-2g(x)]$ ?

Answer: $-2g'(x)$ . Apply constant multiple rule: pull out -2.

Flashcard 23: What is $rac{d}{dx}[5f(x)]$ ?

Answer: $5f'(x)$ . Apply constant multiple rule: pull out 5.

Flashcard 24: What is $rac{d}{dx}[-3]$ ?

Answer: $0$ . -3 is a constant, so its derivative is 0.

Flashcard 25: What is $rac{d}{dx}[7]$ ?

Answer: $0$ . 7 is a constant, so its derivative is 0.

Flashcard 26: State the difference rule: What is $rac{d}{dx}[f(x)-g(x)]$ ?

Answer: $f'(x)-g'(x)$ . Differentiate each term separately and subtract.

Flashcard 27: State the sum rule: What is $rac{d}{dx}[f(x)+g(x)]$ ?

Answer: $f'(x)+g'(x)$ . Differentiate each term separately and add.

Flashcard 28: What is $rac{d}{dx}[3f(x)-2g(x)]$ ?

Answer: $3f'(x)-2g'(x)$ . Apply constant multiple rule to each term.

Flashcard 29: State the constant multiple rule: What is $rac{d}{dx}[c ext{ }f(x)]$ for constant $c$ ?

Answer: $c ext{ }f'(x)$ . Pull out the constant and multiply by the derivative.

Flashcard 30: State the constant rule: What is $rac{d}{dx}[c]$ for a constant $c$ ?

Answer: $0$ . The derivative of any constant is zero.

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AP Calculus AB Flashcards: Derivative Rules Of Constant Sum Difference

Study Derivative Rules Of Constant Sum Difference in AP Calculus AB with focused flashcards that help you recognize the idea, recall the key rule, and apply it in practice-style prompts.

← Back to flashcard decks

What this deck covers

This deck focuses on Derivative Rules Of Constant Sum Difference, giving you a quick way to review the definitions, rules, and examples that matter most for AP Calculus AB.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

AP Calculus AB Flashcards: Derivative Rules Of Constant Sum Difference

/ 30

0 reviewed

0% Complete

0 reviewing

QUESTION

Given $f(x) = x^2 + 3x$ , find $f'(x)$ .

Tap or drag to reveal answer

ANSWER

2x + 3. Apply power rule to each term separately.

Swipe Right = I Know It! 🎉

Swipe Left = Still Learning

All flashcards

Flashcard 1: Given $f(x) = x^2 + 3x$ , find $f'(x)$ .

Answer: 2x + 3. Apply power rule to each term separately.

Flashcard 2: What is the derivative of a constant $c$ with respect to $x$ ?

Answer:

Constants have zero rate of change.

Flashcard 3: Calculate the derivative of $7x^3 - 4x$ .

Answer: 21x^2 - 4. Use power rule: $7 \cdot 3x^2 - 4 = 21x^2 - 4$ .

Flashcard 4: State the derivative of the function $-5$ .

Answer:

Any constant has derivative zero.

Flashcard 5: Calculate the derivative of $12x$ .

Answer:

Derivative of linear term $12x$ is the coefficient.

Flashcard 6: What is the derivative of a constant multiplied by $x$ , $7x$ ?

Answer:

Constant multiple rule: derivative of $cx$ is $c$ .

Flashcard 7: Find the derivative of $8x - 2$ .

Answer:

Derivative of linear term is its coefficient.

Flashcard 8: State the derivative of $x^n$ where $n$ is a constant.

Answer: $nx^{n-1}$ . Power rule: bring down exponent, reduce by 1.

Flashcard 9: Given $f(x) = x^2 + 3x$ , find $f'(x)$ .

Answer: 2x + 3. Apply power rule to each term separately.

Flashcard 10: What is the derivative of $cf(x)$ , where $c$ is a constant?

Answer: $(cf)' = cf'$ . Constant multiple rule: factor out the constant.

Flashcard 11: State the derivative rule for the difference of two functions $f(x)$ and $g(x)$ .

Answer: $(f - g)' = f' - g'$ . Derivative of difference equals difference of derivatives.

Flashcard 12: What is the derivative of a constant $c$ with respect to $x$ ?

Answer:

Constants have zero rate of change.

Flashcard 13: Calculate the derivative of $5x - 3$ .

Answer:

Derivative of linear function is the coefficient of $x$ .

Flashcard 14: State the derivative rule for the sum of two functions $f(x)$ and $g(x)$ .

Answer: $(f + g)' = f' + g'$ . Derivative of sum equals sum of derivatives.

Flashcard 15: Calculate the derivative of $7x^3 - 4x$ .

Answer: 21x^2 - 4. Use power rule: $7 \cdot 3x^2 - 4 = 21x^2 - 4$ .

Flashcard 16: Find the derivative of $8x - 2$ .

Answer:

Derivative of linear term is its coefficient.

Flashcard 17: What is $rac{d}{dx}[2f(x)+3g(x)-5]$ ?

Answer: $2f'(x)+3g'(x)$ . Constant -5 has derivative 0; apply rules to rest.

Flashcard 18: What is $rac{d}{dx}[f(x)-g(x)+h(x)]$ ?

Answer: $f'(x)-g'(x)+h'(x)$ . Apply sum/difference rules term by term.

Flashcard 19: What is $rac{d}{dx}[f(x)+g(x)+h(x)]$ ?

Answer: $f'(x)+g'(x)+h'(x)$ . Sum rule extends to any number of functions.

Flashcard 20: What is $rac{d}{dx}[12-g(x)]$ ?

Answer: $-g'(x)$ . Derivative of 12 is 0; $-g(x)$ gives $-g'(x)$ .

Flashcard 21: What is $rac{d}{dx}[f(x)+9]$ ?

Answer: $f'(x)$ . Derivative of constant 9 is 0, leaving $f'(x)$ .

Flashcard 22: What is $rac{d}{dx}[-2g(x)]$ ?

Answer: $-2g'(x)$ . Apply constant multiple rule: pull out -2.

Flashcard 23: What is $rac{d}{dx}[5f(x)]$ ?

Answer: $5f'(x)$ . Apply constant multiple rule: pull out 5.

Flashcard 24: What is $rac{d}{dx}[-3]$ ?

Answer: $0$ . -3 is a constant, so its derivative is 0.

Flashcard 25: What is $rac{d}{dx}[7]$ ?

Answer: $0$ . 7 is a constant, so its derivative is 0.

Flashcard 26: State the difference rule: What is $rac{d}{dx}[f(x)-g(x)]$ ?

Answer: $f'(x)-g'(x)$ . Differentiate each term separately and subtract.

Flashcard 27: State the sum rule: What is $rac{d}{dx}[f(x)+g(x)]$ ?

Answer: $f'(x)+g'(x)$ . Differentiate each term separately and add.

Flashcard 28: What is $rac{d}{dx}[3f(x)-2g(x)]$ ?

Answer: $3f'(x)-2g'(x)$ . Apply constant multiple rule to each term.

Flashcard 29: State the constant multiple rule: What is $rac{d}{dx}[c ext{ }f(x)]$ for constant $c$ ?

Answer: $c ext{ }f'(x)$ . Pull out the constant and multiply by the derivative.

Flashcard 30: State the constant rule: What is $rac{d}{dx}[c]$ for a constant $c$ ?

Answer: $0$ . The derivative of any constant is zero.

Opening subject page...

AP Calculus AB Flashcards: Derivative Rules Of Constant Sum Difference

What this deck covers

How to use these flashcards

AP Calculus AB Flashcards: Derivative Rules Of Constant Sum Difference

All flashcards

Flashcard 1: Given f(x)=x2+3xf(x) = x^2 + 3xf(x)=x2+3x, find f′(x)f'(x)f′(x).

Flashcard 2: What is the derivative of a constant ccc with respect to xxx?

Flashcard 3: Calculate the derivative of 7x3−4x7x^3 - 4x7x3−4x.

Flashcard 4: State the derivative of the function −5-5−5.

Flashcard 5: Calculate the derivative of 12x12x12x.

Flashcard 6: What is the derivative of a constant multiplied by xxx, 7x7x7x?

Flashcard 7: Find the derivative of 8x−28x - 28x−2.

Flashcard 8: State the derivative of xnx^nxn where nnn is a constant.

Flashcard 9: Given f(x)=x2+3xf(x) = x^2 + 3xf(x)=x2+3x, find f′(x)f'(x)f′(x).

Flashcard 10: What is the derivative of cf(x)cf(x)cf(x), where ccc is a constant?

Flashcard 11: State the derivative rule for the difference of two functions f(x)f(x)f(x) and g(x)g(x)g(x).

Flashcard 12: What is the derivative of a constant ccc with respect to xxx?

Flashcard 13: Calculate the derivative of 5x−35x - 35x−3.

Flashcard 14: State the derivative rule for the sum of two functions f(x)f(x)f(x) and g(x)g(x)g(x).

Flashcard 15: Calculate the derivative of 7x3−4x7x^3 - 4x7x3−4x.

Flashcard 16: Find the derivative of 8x−28x - 28x−2.

Flashcard 17: What is rac{d}{dx}[2f(x)+3g(x)-5]?

Flashcard 18: What is rac{d}{dx}[f(x)-g(x)+h(x)]?

Flashcard 19: What is rac{d}{dx}[f(x)+g(x)+h(x)]?

Flashcard 20: What is rac{d}{dx}[12-g(x)]?

Flashcard 21: What is rac{d}{dx}[f(x)+9]?

Flashcard 22: What is rac{d}{dx}[-2g(x)]?

Flashcard 23: What is rac{d}{dx}[5f(x)]?

Flashcard 24: What is rac{d}{dx}[-3]?

Flashcard 25: What is rac{d}{dx}[7]?

Flashcard 26: State the difference rule: What is rac{d}{dx}[f(x)-g(x)]?

Flashcard 27: State the sum rule: What is rac{d}{dx}[f(x)+g(x)]?

Flashcard 28: What is rac{d}{dx}[3f(x)-2g(x)]?

Flashcard 29: State the constant multiple rule: What is rac{d}{dx}[c ext{ }f(x)] for constant ccc?

Flashcard 30: State the constant rule: What is rac{d}{dx}[c] for a constant ccc?

Opening subject page...

AP Calculus AB Flashcards: Derivative Rules Of Constant Sum Difference

What this deck covers

How to use these flashcards

AP Calculus AB Flashcards: Derivative Rules Of Constant Sum Difference

All flashcards

Flashcard 1: Given f(x)=x2+3xf(x) = x^2 + 3xf(x)=x2+3x, find f′(x)f'(x)f′(x).

Flashcard 2: What is the derivative of a constant ccc with respect to xxx?

Flashcard 3: Calculate the derivative of 7x3−4x7x^3 - 4x7x3−4x.

Flashcard 4: State the derivative of the function −5-5−5.

Flashcard 5: Calculate the derivative of 12x12x12x.

Flashcard 6: What is the derivative of a constant multiplied by xxx, 7x7x7x?

Flashcard 7: Find the derivative of 8x−28x - 28x−2.

Flashcard 8: State the derivative of xnx^nxn where nnn is a constant.

Flashcard 9: Given f(x)=x2+3xf(x) = x^2 + 3xf(x)=x2+3x, find f′(x)f'(x)f′(x).

Flashcard 10: What is the derivative of cf(x)cf(x)cf(x), where ccc is a constant?

Flashcard 11: State the derivative rule for the difference of two functions f(x)f(x)f(x) and g(x)g(x)g(x).

Flashcard 12: What is the derivative of a constant ccc with respect to xxx?

Flashcard 13: Calculate the derivative of 5x−35x - 35x−3.

Flashcard 14: State the derivative rule for the sum of two functions f(x)f(x)f(x) and g(x)g(x)g(x).

Flashcard 15: Calculate the derivative of 7x3−4x7x^3 - 4x7x3−4x.

Flashcard 16: Find the derivative of 8x−28x - 28x−2.

Flashcard 17: What is rac{d}{dx}[2f(x)+3g(x)-5]?

Flashcard 18: What is rac{d}{dx}[f(x)-g(x)+h(x)]?

Flashcard 19: What is rac{d}{dx}[f(x)+g(x)+h(x)]?

Flashcard 20: What is rac{d}{dx}[12-g(x)]?

Flashcard 21: What is rac{d}{dx}[f(x)+9]?

Flashcard 22: What is rac{d}{dx}[-2g(x)]?

Flashcard 23: What is rac{d}{dx}[5f(x)]?

Flashcard 24: What is rac{d}{dx}[-3]?

Flashcard 25: What is rac{d}{dx}[7]?

Flashcard 26: State the difference rule: What is rac{d}{dx}[f(x)-g(x)]?

Flashcard 27: State the sum rule: What is rac{d}{dx}[f(x)+g(x)]?

Flashcard 28: What is rac{d}{dx}[3f(x)-2g(x)]?

Flashcard 29: State the constant multiple rule: What is rac{d}{dx}[c ext{ }f(x)] for constant ccc?

Flashcard 30: State the constant rule: What is rac{d}{dx}[c] for a constant ccc?

Flashcard 1: Given $f(x) = x^2 + 3x$ , find $f'(x)$ .

Flashcard 2: What is the derivative of a constant $c$ with respect to $x$ ?

Flashcard 3: Calculate the derivative of $7x^3 - 4x$ .

Flashcard 4: State the derivative of the function $-5$ .

Flashcard 5: Calculate the derivative of $12x$ .

Flashcard 6: What is the derivative of a constant multiplied by $x$ , $7x$ ?

Flashcard 7: Find the derivative of $8x - 2$ .

Flashcard 8: State the derivative of $x^n$ where $n$ is a constant.

Flashcard 9: Given $f(x) = x^2 + 3x$ , find $f'(x)$ .

Flashcard 10: What is the derivative of $cf(x)$ , where $c$ is a constant?

Flashcard 11: State the derivative rule for the difference of two functions $f(x)$ and $g(x)$ .

Flashcard 12: What is the derivative of a constant $c$ with respect to $x$ ?

Flashcard 13: Calculate the derivative of $5x - 3$ .

Flashcard 14: State the derivative rule for the sum of two functions $f(x)$ and $g(x)$ .

Flashcard 15: Calculate the derivative of $7x^3 - 4x$ .

Flashcard 16: Find the derivative of $8x - 2$ .

Flashcard 17: What is $rac{d}{dx}[2f(x)+3g(x)-5]$ ?

Flashcard 18: What is $rac{d}{dx}[f(x)-g(x)+h(x)]$ ?

Flashcard 19: What is $rac{d}{dx}[f(x)+g(x)+h(x)]$ ?

Flashcard 20: What is $rac{d}{dx}[12-g(x)]$ ?

Flashcard 21: What is $rac{d}{dx}[f(x)+9]$ ?

Flashcard 22: What is $rac{d}{dx}[-2g(x)]$ ?

Flashcard 23: What is $rac{d}{dx}[5f(x)]$ ?

Flashcard 24: What is $rac{d}{dx}[-3]$ ?

Flashcard 25: What is $rac{d}{dx}[7]$ ?

Flashcard 26: State the difference rule: What is $rac{d}{dx}[f(x)-g(x)]$ ?

Flashcard 27: State the sum rule: What is $rac{d}{dx}[f(x)+g(x)]$ ?

Flashcard 28: What is $rac{d}{dx}[3f(x)-2g(x)]$ ?

Flashcard 29: State the constant multiple rule: What is $rac{d}{dx}[c ext{ }f(x)]$ for constant $c$ ?

Flashcard 30: State the constant rule: What is $rac{d}{dx}[c]$ for a constant $c$ ?

Flashcard 1: Given $f(x) = x^2 + 3x$ , find $f'(x)$ .

Flashcard 2: What is the derivative of a constant $c$ with respect to $x$ ?

Flashcard 3: Calculate the derivative of $7x^3 - 4x$ .

Flashcard 4: State the derivative of the function $-5$ .

Flashcard 5: Calculate the derivative of $12x$ .

Flashcard 6: What is the derivative of a constant multiplied by $x$ , $7x$ ?

Flashcard 7: Find the derivative of $8x - 2$ .

Flashcard 8: State the derivative of $x^n$ where $n$ is a constant.

Flashcard 9: Given $f(x) = x^2 + 3x$ , find $f'(x)$ .

Flashcard 10: What is the derivative of $cf(x)$ , where $c$ is a constant?

Flashcard 11: State the derivative rule for the difference of two functions $f(x)$ and $g(x)$ .

Flashcard 12: What is the derivative of a constant $c$ with respect to $x$ ?

Flashcard 13: Calculate the derivative of $5x - 3$ .

Flashcard 14: State the derivative rule for the sum of two functions $f(x)$ and $g(x)$ .

Flashcard 15: Calculate the derivative of $7x^3 - 4x$ .

Flashcard 16: Find the derivative of $8x - 2$ .

Flashcard 17: What is $rac{d}{dx}[2f(x)+3g(x)-5]$ ?

Flashcard 18: What is $rac{d}{dx}[f(x)-g(x)+h(x)]$ ?

Flashcard 19: What is $rac{d}{dx}[f(x)+g(x)+h(x)]$ ?

Flashcard 20: What is $rac{d}{dx}[12-g(x)]$ ?

Flashcard 21: What is $rac{d}{dx}[f(x)+9]$ ?

Flashcard 22: What is $rac{d}{dx}[-2g(x)]$ ?

Flashcard 23: What is $rac{d}{dx}[5f(x)]$ ?

Flashcard 24: What is $rac{d}{dx}[-3]$ ?

Flashcard 25: What is $rac{d}{dx}[7]$ ?

Flashcard 26: State the difference rule: What is $rac{d}{dx}[f(x)-g(x)]$ ?

Flashcard 27: State the sum rule: What is $rac{d}{dx}[f(x)+g(x)]$ ?

Flashcard 28: What is $rac{d}{dx}[3f(x)-2g(x)]$ ?

Flashcard 29: State the constant multiple rule: What is $rac{d}{dx}[c ext{ }f(x)]$ for constant $c$ ?

Flashcard 30: State the constant rule: What is $rac{d}{dx}[c]$ for a constant $c$ ?