AP Calculus AB Product Rule, Quotient Rule and Trig Derivatives Quiz: 10 Questions with Explanations

AP Calculus AB math quiz: Product Rule, Quotient Rule and Trig Derivatives – Maths PDF

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This product quotient quiz for AP Calculus AB covers product rule, quotient rule and trig derivatives (Common Core AP CALC AB 2.8, AP CALC AB 2.9, AP CALC AB 2.10), with a free PDF to print.

Test yourself on the product rule, the quotient rule and the derivatives of tan x, cot x, sec x and csc x 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 2.8, AP CALC AB 2.9, AP CALC AB 2.10

Product quotient quiz: 10 questions

Question 1

What is the derivative of \(f(x)=x\,e^{x}\)?

Question 2

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

Question 3

Which is the correct quotient rule?

Question 4

What is the derivative of \(f(x)=\frac{x}{x^{2}+1}\) at \(x=0\)?

Question 5

Graph of tan x.

What is the slope of \(y=\tan x\) at \(x=0\)?

Question 6

What is \(\frac{d}{dx}[\sec x]\)?

Question 7

What is \(\frac{d}{dx}[\cot x]\)?

Question 8

Graph of f(x) = x sin x.

What is \(f^{\prime}(\pi)\) for \(f(x)=x\sin x\)?

Question 9

If \(f(3)=2\), \(f^{\prime}(3)=5\), \(g(3)=4\) and \(g^{\prime}(3)=-1\), what is \((fg)^{\prime}(3)\)?

Question 10

Values at x = 2.

Using the table, what is \(\left(\frac{f}{g}\right)^{\prime}(2)\)?

Remember

Product rule: (uv)′ = u′v + uv′.
Quotient rule: (u/v)′ = (u′v – uv′)/v², and the order in the numerator matters.
d/dx tan x = sec²x and d/dx sec x = sec x tan x.
The derivatives of cot x and csc x are negative: -csc²x and -csc x cot x.

How to use this product quotient 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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