AP Calculus AB Derivatives of Inverse Functions Quiz: 10 Questions with Explanations

AP Calculus AB math quiz: Derivatives of Inverse Functions – Maths PDF

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This inverse derivatives quiz for AP Calculus AB covers derivatives of inverse functions (Common Core AP CALC AB 3.3, AP CALC AB 3.4, AP CALC AB 3.5, AP CALC AB 3.6), with a free PDF to print.

Test yourself on derivatives of inverse functions, derivatives of inverse trigonometric functions, choosing differentiation methods and higher-order derivatives with 10 multiple-choice questions. Pick one answer for each question, then read the explanation to see why it is right and which common mistake the other choices represent.

AP Calculus AB · Common Core State Standards: AP CALC AB 3.3, AP CALC AB 3.4, AP CALC AB 3.5, AP CALC AB 3.6

Inverse derivatives quiz: 10 questions

Question 1

If \(f(3)=7\) and \(f^{\prime}(3)=5\), what is \(\left(f^{-1}\right)^{\prime}(7)\)?

Question 2

Values of f.

Using the table, what is \(\left(f^{-1}\right)^{\prime}(6)\)?

Question 3

What is \(\frac{d}{dx}\left[\tan^{-1}x\right]\)?

Question 4

What is \(\frac{d}{dx}\left[\sin^{-1}x\right]\)?

Question 5

arctan x and its derivative.

Where is the slope of \(y=\tan^{-1}x\) greatest?

Question 6

What is \(\frac{d}{dx}\left[\sin^{-1}(2x)\right]\)?

Question 7

What is the second derivative of \(f(x)=x^{4}\)?

Question 8

Position of a particle.

A particle has position \(s(t)=t^{3}-6t^{2}+9t\). What is its acceleration at \(t=2\)?

Question 9

What is \(\frac{d^{2}}{dx^{2}}[e^{2x}]\)?

Question 10

Which rule is best for \(\frac{x^{2}}{\cos x}\)?

Remember

(f⁻¹)′(b) = 1/f′(a) where f(a) = b; evaluate f′ at a, not at b.
d/dx sin⁻¹x = 1/√(1-x²), d/dx cos⁻¹x = -1/√(1-x²), d/dx tan⁻¹x = 1/(1+x²).
The second derivative is the derivative of the first derivative; acceleration is the second derivative of position.
Choose the rule by the outermost operation: sum, product, quotient or composition.

How to use this inverse derivatives quiz

Answer each question, read the explanation that appears, and keep track of your score. A score of 8 out of 10 or more means you are ready for the test.

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