Calculus · Practice

Derivatives — Exercises

Graded practice problems from foundations to advanced. Enter your answer and press Check.

Foundations

Problem 1

Let $f(x) = 3x^2$ . Find $f'(1)$ .

Problem 2

Let $f(x) = x^3$ . Find $f'(2)$ .

Problem 3

Find $\dfrac{d}{dx}(7)$ .

Problem 4

Find $\dfrac{d}{dx}(2x + 3)$ .

Problem 5

Let $f(x) = \sin x$ . Find $f'(0)$ .

Problem 6

Let $f(x) = 2x^4$ . Find $f'(1)$ .

Problem 7

Let $f(x) = \cos x$ . Find $f'\!\left(\dfrac{\pi}{2}\right)$ .

Problem 8

Let $f(x) = e^{2x}$ . Find $f'(0)$ .

Problem 9

Find the larger critical point of $f(x) = x^3 - 6x^2 + 9x + 1$ .

Problem 10

For the circle $x^2 + y^2 = 25$ , find the positive $y$ -value when $x = 3$ .

(This is also the $y$ -intercept needed for implicit differentiation at the point $(3, 4)$ .)

Problem 11

Use implicit differentiation on $x^2 + y^2 = 25$ to find $\dfrac{dy}{dx}$ at the point $(3, 4)$ .