AP Calculus AB Power, Sum and Basic Function Derivative Rules Quiz: 10 Questions with Explanations

AP Calculus AB math quiz: Power, Sum and Basic Function Derivative Rules – Maths PDF

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This derivative rules quiz for AP Calculus AB covers power, sum and basic function derivative rules (Common Core AP CALC AB 2.5, AP CALC AB 2.6, AP CALC AB 2.7), with a free PDF to print.

Test yourself on the power rule, sum and constant multiple rules, derivatives of sin x, cos x, e^x and ln x, and tangent and normal lines 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 2.5, AP CALC AB 2.6, AP CALC AB 2.7

Derivative rules quiz: 10 questions

Question 1

What is \(\frac{d}{dx}\left[x^{7}\right]\)?

Question 2

What is the derivative of \(f(x)=5x^{3}-4x+9\)?

Question 3

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

Question 4

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

Question 5

Tangent to ln x at x = 4.

What is the slope of the tangent to \(y=\ln x\) at \(x=4\)?

Question 6

What is \(\frac{d}{dx}[\ln x]\) at \(x=4\)?

Question 7

Graph of f(x) = x² − 4x.

Where does \(f(x)=x^{2}-4x\) have a horizontal tangent?

Question 8

What is the tangent line to \(f(x)=x^{3}\) at \(x=1\)?

Question 9

What is the slope of the normal line to \(f(x)=x^{2}\) at \(x=3\)?

Question 10

Graph of f(x) = x³ − 3x.

At how many points does the graph of \(f(x)=x^{3}-3x\) have a horizontal tangent?

Remember

Power rule: d/dx of x^n equals n x^(n-1); the derivative of a constant is 0.
Rewrite roots and reciprocals as powers before differentiating.
The derivatives of sin x, cos x, e^x and ln x are cos x, -sin x, e^x and 1/x.
A normal line has slope equal to the negative reciprocal of the tangent slope.

How to use this derivative rules 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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