Advanced · Algebra & functions

Derivative rules practice

Derivative rules is an advanced math skill: apply the power, product, quotient, and chain rules to differentiate functions. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 27 derivative rules problems our math games drill.

27 questions in the bank

Sample questions

Try 8 for free

Question 1easy

If $f(x) = x^{3}$ , what is $f'(2)$ ?

$f'(x) = 3x^{2}$ , so $f'(2) = 3 \cdot 2^{2} = 12$ .

Question 2easy

Find $\dfrac{d}{dx}\left[x^2 \sin x\right]$ .

Product rule: $(fg)' = f'g + fg' = 2x\sin x + x^2\cos x$ .

Question 3easy

If $f(x) = 2x^{2}$ , what is $f'(3)$ ?

$f'(x) = 4x^{1}$ , so $f'(3) = 4 \cdot 3^{1} = 12$ .

Question 4easy

If $f(x) = x^{2}$ , what is $f'(5)$ ?

$f'(x) = 2x^{1}$ , so $f'(5) = 2 \cdot 5^{1} = 10$ .

Question 5easy

If $f(x) = x^{4}$ , what is $f'(1)$ ?

$f'(x) = 4x^{3}$ , so $f'(1) = 4 \cdot 1^{3} = 4$ .

Question 6easy

If $f(x) = 3x^{2}$ , what is $f'(2)$ ?

$f'(x) = 6x^{1}$ , so $f'(2) = 6 \cdot 2^{1} = 12$ .

Question 7easy

If $f(x) = x^{3}$ , what is $f'(1)$ ?

$f'(x) = 3x^{2}$ , so $f'(1) = 3 \cdot 1^{2} = 3$ .

Question 8easy

If $f(x) = 2x^{3}$ , what is $f'(1)$ ?

$f'(x) = 6x^{2}$ , so $f'(1) = 6 \cdot 1^{2} = 6$ .

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