Home

Tutoring

Subjects

Live Classes

Study Coach

Essay Review

On-Demand Courses

Colleges

Games

Opening subject page...

Loading your content

Home

Tutoring

Subjects

Live Classes

Study Coach

Essay Review

On-Demand Courses

Colleges

Games

AP Calculus BC Flashcards: Derivative Rules Of Constant Sum Difference

Study Derivative Rules Of Constant Sum Difference in AP Calculus BC 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 BC.

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 BC Flashcards: Derivative Rules Of Constant Sum Difference

/ 30

0 reviewed

0% Complete

0 reviewing

QUESTION

Find $\frac{d}{dx}[3x^3 - 4x + 5]$ .

Tap or drag to reveal answer

ANSWER

9x^2 - 4. Differentiate each term using power rule.

Swipe Right = I Know It! 🎉

Swipe Left = Still Learning

All flashcards

Flashcard 1: Find $\frac{d}{dx}[3x^3 - 4x + 5]$ .

Answer: 9x^2 - 4. Differentiate each term using power rule.

Flashcard 2: Find the derivative of $f(x) = 7x^3$ .

Answer: 21x^2. Apply constant multiple rule: $7 \cdot 3x^2 = 21x^2$ .

Flashcard 3: Find the derivative of $f(x) = x^3 + x^2 + x$ .

Answer: 3x^2 + 2x + 1. Apply power rule to each term.

Flashcard 4: What is the derivative of $f(x) = x^2 - 2x$ ?

Answer: 2x - 2. Apply difference rule: $2x - 2$ .

Flashcard 5: Find the derivative of $f(x) = 7x^3$ .

Answer: 21x^2. Apply constant multiple rule: $7 \cdot 3x^2 = 21x^2$ .

Flashcard 6: State the derivative of $f(x) = 3x^2 + 2x$ .

Answer: 6x + 2. Apply power rule to each term.

Flashcard 7: Find the derivative of $f(x) = 3 - x^3$ .

Answer: $-3x^2$ . Constant term has zero derivative.

Flashcard 8: What is the derivative of $f(x) = 5x^4$ ?

Answer: 20x^3. Apply constant multiple rule: $5 \cdot 4x^3 = 20x^3$ .

Flashcard 9: What is $\frac{d}{dx}[7]$ ?

Answer:

Any constant has zero derivative.

Flashcard 10: Find $\frac{d}{dx}[3x^3 - 4x + 5]$ .

Answer: 9x^2 - 4. Differentiate each term using power rule.

Flashcard 11: State the derivative of $f(x) = 12$ .

Answer: $0$ . Any constant has zero derivative.

Flashcard 12: What is the derivative of $f(x) = 4x^3 - 9$ ?

Answer: 12x^2. Derivative of $4x^3$ is $12x^2$ , constant disappears.

Flashcard 13: Find $\frac{d}{dx}[2x^2 + 5x + 1]$ .

Answer: $4x + 5$ . Differentiate each term separately.

Flashcard 14: What is the derivative of $f(x) = 3x^3 + 4x$ ?

Answer: 9x^2 + 4. Apply sum rule: $9x^2 + 4$ .

Flashcard 15: Find the derivative of $f(x) = 5x^2$ using the constant multiple rule.

Answer: 10x. Apply constant multiple rule: $5 \cdot 2x = 10x$ .

Flashcard 16: State the derivative of $f(x) = 5x^2 + 4x$ .

Answer: 10x + 4. Apply power rule to each term.

Flashcard 17: State the rule for $\frac{d}{dx}[c]$ where $c$ is a constant.

Answer:

Constants have zero rate of change.

Flashcard 18: What is the derivative of $f(x) = x^2 - 4x + 4$ ?

Answer: 2x - 4. Differentiate each term, constant disappears.

Flashcard 19: Find the derivative of $f(x) = 6$ .

Answer:

Any constant has derivative zero.

Flashcard 20: What is the result of $\frac{d}{dx}[4x^3]$ ?

Answer: 12x^2. Apply constant multiple rule: $4 \cdot 3x^2 = 12x^2$ .

Flashcard 21: What is the derivative of $f(x) = 2x^2 - 3x + 1$ ?

Answer: 4x - 3. Differentiate each term, constant disappears.

Flashcard 22: What is the derivative of $f(x) = 6x^2 + 7$ ?

Answer: 12x. Derivative of $6x^2$ is $12x$ , constant disappears.

Flashcard 23: Find the derivative of $f(x) = 10$ .

Answer:

Any constant has zero derivative.

Flashcard 24: State the derivative of $f(x) = 2x^2$ using the constant multiple rule.

Answer: 4x. Apply constant multiple rule: $2 \cdot 2x = 4x$ .

Flashcard 25: What is the derivative of $f(x) = 5x + 6$ ?

Answer:

Derivative of $5x$ is $5$ , constant disappears.

Flashcard 26: State the derivative of $f(x) = 0$ .

Answer:

Zero function has zero derivative.

Flashcard 27: Find the derivative of $f(x) = 4x^2 - 7x$ .

Answer: 8x - 7. Apply power rule to each term.

Flashcard 28: State the sum rule for derivatives.

Answer: $\frac{d}{dx}[f(x) + g(x)] = f'(x) + g'(x)$ . Derivative of sum equals sum of derivatives.

Flashcard 29: What is the derivative of $f(x) = 9x$ ?

Answer:

Derivative of $x$ is $1$ , multiply by $9$ .

Flashcard 30: What is the derivative of $f(x) = 2x + 3x^2$ ?

Answer: 2 + 6x. Apply sum rule to each term.

Opening subject page...

Loading your content

AP Calculus BC Flashcards: Derivative Rules Of Constant Sum Difference

Study Derivative Rules Of Constant Sum Difference in AP Calculus BC 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 BC.

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 BC Flashcards: Derivative Rules Of Constant Sum Difference

/ 30

0 reviewed

0% Complete

0 reviewing

QUESTION

Find $\frac{d}{dx}[3x^3 - 4x + 5]$ .

Tap or drag to reveal answer

ANSWER

9x^2 - 4. Differentiate each term using power rule.

Swipe Right = I Know It! 🎉

Swipe Left = Still Learning

All flashcards

Flashcard 1: Find $\frac{d}{dx}[3x^3 - 4x + 5]$ .

Answer: 9x^2 - 4. Differentiate each term using power rule.

Flashcard 2: Find the derivative of $f(x) = 7x^3$ .

Answer: 21x^2. Apply constant multiple rule: $7 \cdot 3x^2 = 21x^2$ .

Flashcard 3: Find the derivative of $f(x) = x^3 + x^2 + x$ .

Answer: 3x^2 + 2x + 1. Apply power rule to each term.

Flashcard 4: What is the derivative of $f(x) = x^2 - 2x$ ?

Answer: 2x - 2. Apply difference rule: $2x - 2$ .

Flashcard 5: Find the derivative of $f(x) = 7x^3$ .

Answer: 21x^2. Apply constant multiple rule: $7 \cdot 3x^2 = 21x^2$ .

Flashcard 6: State the derivative of $f(x) = 3x^2 + 2x$ .

Answer: 6x + 2. Apply power rule to each term.

Flashcard 7: Find the derivative of $f(x) = 3 - x^3$ .

Answer: $-3x^2$ . Constant term has zero derivative.

Flashcard 8: What is the derivative of $f(x) = 5x^4$ ?

Answer: 20x^3. Apply constant multiple rule: $5 \cdot 4x^3 = 20x^3$ .

Flashcard 9: What is $\frac{d}{dx}[7]$ ?

Answer:

Any constant has zero derivative.

Flashcard 10: Find $\frac{d}{dx}[3x^3 - 4x + 5]$ .

Answer: 9x^2 - 4. Differentiate each term using power rule.

Flashcard 11: State the derivative of $f(x) = 12$ .

Answer: $0$ . Any constant has zero derivative.

Flashcard 12: What is the derivative of $f(x) = 4x^3 - 9$ ?

Answer: 12x^2. Derivative of $4x^3$ is $12x^2$ , constant disappears.

Flashcard 13: Find $\frac{d}{dx}[2x^2 + 5x + 1]$ .

Answer: $4x + 5$ . Differentiate each term separately.

Flashcard 14: What is the derivative of $f(x) = 3x^3 + 4x$ ?

Answer: 9x^2 + 4. Apply sum rule: $9x^2 + 4$ .

Flashcard 15: Find the derivative of $f(x) = 5x^2$ using the constant multiple rule.

Answer: 10x. Apply constant multiple rule: $5 \cdot 2x = 10x$ .

Flashcard 16: State the derivative of $f(x) = 5x^2 + 4x$ .

Answer: 10x + 4. Apply power rule to each term.

Flashcard 17: State the rule for $\frac{d}{dx}[c]$ where $c$ is a constant.

Answer:

Constants have zero rate of change.

Flashcard 18: What is the derivative of $f(x) = x^2 - 4x + 4$ ?

Answer: 2x - 4. Differentiate each term, constant disappears.

Flashcard 19: Find the derivative of $f(x) = 6$ .

Answer:

Any constant has derivative zero.

Flashcard 20: What is the result of $\frac{d}{dx}[4x^3]$ ?

Answer: 12x^2. Apply constant multiple rule: $4 \cdot 3x^2 = 12x^2$ .

Flashcard 21: What is the derivative of $f(x) = 2x^2 - 3x + 1$ ?

Answer: 4x - 3. Differentiate each term, constant disappears.

Flashcard 22: What is the derivative of $f(x) = 6x^2 + 7$ ?

Answer: 12x. Derivative of $6x^2$ is $12x$ , constant disappears.

Flashcard 23: Find the derivative of $f(x) = 10$ .

Answer:

Any constant has zero derivative.

Flashcard 24: State the derivative of $f(x) = 2x^2$ using the constant multiple rule.

Answer: 4x. Apply constant multiple rule: $2 \cdot 2x = 4x$ .

Flashcard 25: What is the derivative of $f(x) = 5x + 6$ ?

Answer:

Derivative of $5x$ is $5$ , constant disappears.

Flashcard 26: State the derivative of $f(x) = 0$ .

Answer:

Zero function has zero derivative.

Flashcard 27: Find the derivative of $f(x) = 4x^2 - 7x$ .

Answer: 8x - 7. Apply power rule to each term.

Flashcard 28: State the sum rule for derivatives.

Answer: $\frac{d}{dx}[f(x) + g(x)] = f'(x) + g'(x)$ . Derivative of sum equals sum of derivatives.

Flashcard 29: What is the derivative of $f(x) = 9x$ ?

Answer:

Derivative of $x$ is $1$ , multiply by $9$ .

Flashcard 30: What is the derivative of $f(x) = 2x + 3x^2$ ?

Answer: 2 + 6x. Apply sum rule to each term.

Opening subject page...

AP Calculus BC Flashcards: Derivative Rules Of Constant Sum Difference

What this deck covers

How to use these flashcards

AP Calculus BC Flashcards: Derivative Rules Of Constant Sum Difference

All flashcards

Flashcard 1: Find ddx[3x3−4x+5]\frac{d}{dx}[3x^3 - 4x + 5]dxd​[3x3−4x+5].

Flashcard 2: Find the derivative of f(x)=7x3f(x) = 7x^3f(x)=7x3.

Flashcard 3: Find the derivative of f(x)=x3+x2+xf(x) = x^3 + x^2 + xf(x)=x3+x2+x.

Flashcard 4: What is the derivative of f(x)=x2−2xf(x) = x^2 - 2xf(x)=x2−2x?

Flashcard 5: Find the derivative of f(x)=7x3f(x) = 7x^3f(x)=7x3.

Flashcard 6: State the derivative of f(x)=3x2+2xf(x) = 3x^2 + 2xf(x)=3x2+2x.

Flashcard 7: Find the derivative of f(x)=3−x3f(x) = 3 - x^3f(x)=3−x3.

Flashcard 8: What is the derivative of f(x)=5x4f(x) = 5x^4f(x)=5x4?

Flashcard 9: What is ddx[7]\frac{d}{dx}[7]dxd​[7]?

Flashcard 10: Find ddx[3x3−4x+5]\frac{d}{dx}[3x^3 - 4x + 5]dxd​[3x3−4x+5].

Flashcard 11: State the derivative of f(x)=12f(x) = 12f(x)=12.

Flashcard 12: What is the derivative of f(x)=4x3−9f(x) = 4x^3 - 9f(x)=4x3−9?

Flashcard 13: Find ddx[2x2+5x+1]\frac{d}{dx}[2x^2 + 5x + 1]dxd​[2x2+5x+1].

Flashcard 14: What is the derivative of f(x)=3x3+4xf(x) = 3x^3 + 4xf(x)=3x3+4x?

Flashcard 15: Find the derivative of f(x)=5x2f(x) = 5x^2f(x)=5x2 using the constant multiple rule.

Flashcard 16: State the derivative of f(x)=5x2+4xf(x) = 5x^2 + 4xf(x)=5x2+4x.

Flashcard 17: State the rule for ddx[c]\frac{d}{dx}[c]dxd​[c] where ccc is a constant.

Flashcard 18: What is the derivative of f(x)=x2−4x+4f(x) = x^2 - 4x + 4f(x)=x2−4x+4?

Flashcard 19: Find the derivative of f(x)=6f(x) = 6f(x)=6.

Flashcard 20: What is the result of ddx[4x3]\frac{d}{dx}[4x^3]dxd​[4x3]?

Flashcard 21: What is the derivative of f(x)=2x2−3x+1f(x) = 2x^2 - 3x + 1f(x)=2x2−3x+1?

Flashcard 22: What is the derivative of f(x)=6x2+7f(x) = 6x^2 + 7f(x)=6x2+7?

Flashcard 23: Find the derivative of f(x)=10f(x) = 10f(x)=10.

Flashcard 24: State the derivative of f(x)=2x2f(x) = 2x^2f(x)=2x2 using the constant multiple rule.

Flashcard 25: What is the derivative of f(x)=5x+6f(x) = 5x + 6f(x)=5x+6?

Flashcard 26: State the derivative of f(x)=0f(x) = 0f(x)=0.

Flashcard 27: Find the derivative of f(x)=4x2−7xf(x) = 4x^2 - 7xf(x)=4x2−7x.

Flashcard 28: State the sum rule for derivatives.

Flashcard 29: What is the derivative of f(x)=9xf(x) = 9xf(x)=9x?

Flashcard 30: What is the derivative of f(x)=2x+3x2f(x) = 2x + 3x^2f(x)=2x+3x2?

Opening subject page...

AP Calculus BC Flashcards: Derivative Rules Of Constant Sum Difference

What this deck covers

How to use these flashcards

AP Calculus BC Flashcards: Derivative Rules Of Constant Sum Difference

All flashcards

Flashcard 1: Find ddx[3x3−4x+5]\frac{d}{dx}[3x^3 - 4x + 5]dxd​[3x3−4x+5].

Flashcard 2: Find the derivative of f(x)=7x3f(x) = 7x^3f(x)=7x3.

Flashcard 3: Find the derivative of f(x)=x3+x2+xf(x) = x^3 + x^2 + xf(x)=x3+x2+x.

Flashcard 4: What is the derivative of f(x)=x2−2xf(x) = x^2 - 2xf(x)=x2−2x?

Flashcard 5: Find the derivative of f(x)=7x3f(x) = 7x^3f(x)=7x3.

Flashcard 6: State the derivative of f(x)=3x2+2xf(x) = 3x^2 + 2xf(x)=3x2+2x.

Flashcard 7: Find the derivative of f(x)=3−x3f(x) = 3 - x^3f(x)=3−x3.

Flashcard 8: What is the derivative of f(x)=5x4f(x) = 5x^4f(x)=5x4?

Flashcard 9: What is ddx[7]\frac{d}{dx}[7]dxd​[7]?

Flashcard 10: Find ddx[3x3−4x+5]\frac{d}{dx}[3x^3 - 4x + 5]dxd​[3x3−4x+5].

Flashcard 11: State the derivative of f(x)=12f(x) = 12f(x)=12.

Flashcard 12: What is the derivative of f(x)=4x3−9f(x) = 4x^3 - 9f(x)=4x3−9?

Flashcard 13: Find ddx[2x2+5x+1]\frac{d}{dx}[2x^2 + 5x + 1]dxd​[2x2+5x+1].

Flashcard 14: What is the derivative of f(x)=3x3+4xf(x) = 3x^3 + 4xf(x)=3x3+4x?

Flashcard 15: Find the derivative of f(x)=5x2f(x) = 5x^2f(x)=5x2 using the constant multiple rule.

Flashcard 16: State the derivative of f(x)=5x2+4xf(x) = 5x^2 + 4xf(x)=5x2+4x.

Flashcard 17: State the rule for ddx[c]\frac{d}{dx}[c]dxd​[c] where ccc is a constant.

Flashcard 18: What is the derivative of f(x)=x2−4x+4f(x) = x^2 - 4x + 4f(x)=x2−4x+4?

Flashcard 19: Find the derivative of f(x)=6f(x) = 6f(x)=6.

Flashcard 20: What is the result of ddx[4x3]\frac{d}{dx}[4x^3]dxd​[4x3]?

Flashcard 21: What is the derivative of f(x)=2x2−3x+1f(x) = 2x^2 - 3x + 1f(x)=2x2−3x+1?

Flashcard 22: What is the derivative of f(x)=6x2+7f(x) = 6x^2 + 7f(x)=6x2+7?

Flashcard 23: Find the derivative of f(x)=10f(x) = 10f(x)=10.

Flashcard 24: State the derivative of f(x)=2x2f(x) = 2x^2f(x)=2x2 using the constant multiple rule.

Flashcard 25: What is the derivative of f(x)=5x+6f(x) = 5x + 6f(x)=5x+6?

Flashcard 26: State the derivative of f(x)=0f(x) = 0f(x)=0.

Flashcard 27: Find the derivative of f(x)=4x2−7xf(x) = 4x^2 - 7xf(x)=4x2−7x.

Flashcard 28: State the sum rule for derivatives.

Flashcard 29: What is the derivative of f(x)=9xf(x) = 9xf(x)=9x?

Flashcard 30: What is the derivative of f(x)=2x+3x2f(x) = 2x + 3x^2f(x)=2x+3x2?

Flashcard 1: Find $\frac{d}{dx}[3x^3 - 4x + 5]$ .

Flashcard 2: Find the derivative of $f(x) = 7x^3$ .

Flashcard 3: Find the derivative of $f(x) = x^3 + x^2 + x$ .

Flashcard 4: What is the derivative of $f(x) = x^2 - 2x$ ?

Flashcard 5: Find the derivative of $f(x) = 7x^3$ .

Flashcard 6: State the derivative of $f(x) = 3x^2 + 2x$ .

Flashcard 7: Find the derivative of $f(x) = 3 - x^3$ .

Flashcard 8: What is the derivative of $f(x) = 5x^4$ ?

Flashcard 9: What is $\frac{d}{dx}[7]$ ?

Flashcard 10: Find $\frac{d}{dx}[3x^3 - 4x + 5]$ .

Flashcard 11: State the derivative of $f(x) = 12$ .

Flashcard 12: What is the derivative of $f(x) = 4x^3 - 9$ ?

Flashcard 13: Find $\frac{d}{dx}[2x^2 + 5x + 1]$ .

Flashcard 14: What is the derivative of $f(x) = 3x^3 + 4x$ ?

Flashcard 15: Find the derivative of $f(x) = 5x^2$ using the constant multiple rule.

Flashcard 16: State the derivative of $f(x) = 5x^2 + 4x$ .

Flashcard 17: State the rule for $\frac{d}{dx}[c]$ where $c$ is a constant.

Flashcard 18: What is the derivative of $f(x) = x^2 - 4x + 4$ ?

Flashcard 19: Find the derivative of $f(x) = 6$ .

Flashcard 20: What is the result of $\frac{d}{dx}[4x^3]$ ?

Flashcard 21: What is the derivative of $f(x) = 2x^2 - 3x + 1$ ?

Flashcard 22: What is the derivative of $f(x) = 6x^2 + 7$ ?

Flashcard 23: Find the derivative of $f(x) = 10$ .

Flashcard 24: State the derivative of $f(x) = 2x^2$ using the constant multiple rule.

Flashcard 25: What is the derivative of $f(x) = 5x + 6$ ?

Flashcard 26: State the derivative of $f(x) = 0$ .

Flashcard 27: Find the derivative of $f(x) = 4x^2 - 7x$ .

Flashcard 29: What is the derivative of $f(x) = 9x$ ?

Flashcard 30: What is the derivative of $f(x) = 2x + 3x^2$ ?

Flashcard 1: Find $\frac{d}{dx}[3x^3 - 4x + 5]$ .

Flashcard 2: Find the derivative of $f(x) = 7x^3$ .

Flashcard 3: Find the derivative of $f(x) = x^3 + x^2 + x$ .

Flashcard 4: What is the derivative of $f(x) = x^2 - 2x$ ?

Flashcard 5: Find the derivative of $f(x) = 7x^3$ .

Flashcard 6: State the derivative of $f(x) = 3x^2 + 2x$ .

Flashcard 7: Find the derivative of $f(x) = 3 - x^3$ .

Flashcard 8: What is the derivative of $f(x) = 5x^4$ ?

Flashcard 9: What is $\frac{d}{dx}[7]$ ?

Flashcard 10: Find $\frac{d}{dx}[3x^3 - 4x + 5]$ .

Flashcard 11: State the derivative of $f(x) = 12$ .

Flashcard 12: What is the derivative of $f(x) = 4x^3 - 9$ ?

Flashcard 13: Find $\frac{d}{dx}[2x^2 + 5x + 1]$ .

Flashcard 14: What is the derivative of $f(x) = 3x^3 + 4x$ ?

Flashcard 15: Find the derivative of $f(x) = 5x^2$ using the constant multiple rule.

Flashcard 16: State the derivative of $f(x) = 5x^2 + 4x$ .

Flashcard 17: State the rule for $\frac{d}{dx}[c]$ where $c$ is a constant.

Flashcard 18: What is the derivative of $f(x) = x^2 - 4x + 4$ ?

Flashcard 19: Find the derivative of $f(x) = 6$ .

Flashcard 20: What is the result of $\frac{d}{dx}[4x^3]$ ?

Flashcard 21: What is the derivative of $f(x) = 2x^2 - 3x + 1$ ?

Flashcard 22: What is the derivative of $f(x) = 6x^2 + 7$ ?

Flashcard 23: Find the derivative of $f(x) = 10$ .

Flashcard 24: State the derivative of $f(x) = 2x^2$ using the constant multiple rule.

Flashcard 25: What is the derivative of $f(x) = 5x + 6$ ?

Flashcard 26: State the derivative of $f(x) = 0$ .

Flashcard 27: Find the derivative of $f(x) = 4x^2 - 7x$ .

Flashcard 29: What is the derivative of $f(x) = 9x$ ?

Flashcard 30: What is the derivative of $f(x) = 2x + 3x^2$ ?