AP Calculus AB Flashcards: Derivatives Of Reciprocal Trig Functions
Study Derivatives Of Reciprocal Trig Functions in AP Calculus AB with focused flashcards that help you recognize the idea, recall the key rule, and apply it in practice-style prompts.
This deck focuses on Derivatives Of Reciprocal Trig Functions, giving you a quick way to review the definitions, rules, and examples that matter most for AP Calculus AB.
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AP Calculus AB Flashcards: Derivatives Of Reciprocal Trig Functions
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QUESTION
State the derivative of f(x)=cot(3x3).
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ANSWER
−9x2csc2(3x3). Chain rule: multiply by derivative of inner function 9x2.
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Flashcard 1: State the derivative of f(x)=cot(3x3).
Answer: −9x2csc2(3x3). Chain rule: multiply by derivative of inner function 9x2.
Flashcard 2: State the derivative of cot(x).
Answer: −csc2(x). Standard derivative formula for cotangent function.
Flashcard 3: State the derivative of g(x)=sec(x3).
Answer: 3x2sec(x3)tan(x3). Chain rule: multiply by derivative of inner function 3x2.
Flashcard 4: Compute d/dx for g(x)=sec(x2+1).
Answer: 2xsec(x2+1)tan(x2+1). Chain rule: multiply by derivative of inner function 2x.
Flashcard 5: What is the derivative of f(x)=cot(3x)?
Answer: −3csc2(3x). Chain rule: multiply by derivative of inner function 3.
Flashcard 6: What is the derivative of sec(x)?
Answer: sec(x)tan(x). Standard derivative formula for secant function.
Flashcard 7: State d/dx for g(x)=cot(x).
Answer: −2x1csc2(x). Chain rule: multiply by derivative of x which is 2x1.
Flashcard 8: Find d/dx for g(x)=cot(ln(x)).
Answer: −x1csc2(ln(x)). Chain rule: multiply by derivative of ln(x) which is x1.
Flashcard 9: Compute the derivative of g(x)=csc(x4).
Answer: −4x3csc(x4)cot(x4). Chain rule: multiply by derivative of inner function 4x3.
Flashcard 10: Determine the derivative of y=tan(3x2).
Answer: 6xsec2(3x2). Chain rule: multiply by derivative of inner function 6x.
Flashcard 11: What is the derivative of f(x)=tan(x2+1)?
Answer: 2xsec2(x2+1). Chain rule: multiply by derivative of inner function 2x.
Flashcard 12: Identify the derivative of y=tan(x+π).
Answer: sec2(x+π). Chain rule: multiply by derivative of inner function 1.
Flashcard 13: Determine d/dx for y=csc(ex).
Answer: −excsc(ex)cot(ex). Chain rule: multiply by derivative of ex which is ex.
Flashcard 14: Find d/dx for h(x)=sec(3x+1).
Answer: 3sec(3x+1)tan(3x+1). Chain rule: multiply by derivative of inner function 3.
Flashcard 15: Calculate the derivative of y=csc(4x).
Answer: −4csc(4x)cot(4x). Chain rule: multiply by derivative of inner function 4.
Flashcard 16: State the derivative of g(x)=cot(2x3).
Answer: −6x2csc2(2x3). Chain rule: multiply by derivative of inner function 6x2.
Flashcard 17: What is the derivative of f(x)=tan(5x2)?
Answer: 10xsec2(5x2). Chain rule: multiply by derivative of inner function 10x.
Flashcard 18: State the derivative of f(x)=cot(3x3).
Answer: −9x2csc2(3x3). Chain rule: multiply by derivative of inner function 9x2.
Flashcard 19: Find the derivative of h(x)=csc(ln(x)).
Answer: −x1csc(ln(x))cot(ln(x)). Chain rule: multiply by derivative of ln(x) which is x1.
Flashcard 20: Calculate d/dx for g(x)=sec(x5).
Answer: 5x4sec(x5)tan(x5). Chain rule: multiply by derivative of inner function 5x4.
Flashcard 21: What is the derivative of y=cot(ex)?
Answer: −excsc2(ex). Chain rule: multiply by derivative of ex which is ex.
Flashcard 22: Find the derivative of f(x)=tan(ex).
Answer: exsec2(ex). Chain rule: multiply by derivative of ex which is ex.
Flashcard 23: Determine the derivative of y=csc(x2).
Answer: −2xcsc(x2)cot(x2). Chain rule: multiply by derivative of inner function 2x.
Flashcard 24: Compute the derivative of h(x)=sec(ln(x)).
Answer: x1sec(ln(x))tan(ln(x)). Chain rule: multiply by derivative of ln(x) which is x1.
Flashcard 25: Determine the derivative of y=csc(4x2).
Answer: −8xcsc(4x2)cot(4x2). Chain rule: multiply by derivative of inner function 8x.
Flashcard 26: Find d/dx for f(x)=sec(sin(x)).
Answer: cos(x)sec(sin(x))tan(sin(x)). Chain rule: multiply by derivative of sin(x) which is cos(x).
Flashcard 27: Compute the derivative of g(x)=sec(5x).
Answer: 5sec(5x)tan(5x). Chain rule: multiply by derivative of inner function 5.
Flashcard 28: Find d/dx for f(x)=sec2(x).
Answer: 2sec(x)sec(x)tan(x). Chain rule applied to sec2(x)=2sec(x)⋅sec(x)tan(x).
Flashcard 29: What is the derivative of y=cot(x3)?
Answer: −3x2csc2(x3). Chain rule: multiply by derivative of inner function 3x2.
Flashcard 30: Determine d/dx for h(x)=csc(2x).
Answer: −2csc(2x)cot(2x). Chain rule: multiply by derivative of inner function 2.