Practice finding derivatives using the power rule, constant rule, sum rule, product rule, quotient rule, and chain rule.
Find each derivative carefully. Simplify your answers when possible and show your work in the space provided.
Applying basic rules to find rates of change
Math - Grade 9-12
- 1
Find the derivative of f(x) = 7.
- 2
Find the derivative of f(x) = x^5.
- 3
Find the derivative of f(x) = 4x^3 - 2x + 9.
- 4
Find the derivative of f(x) = 6x^4 + x^2 - 8x + 1.
- 5
Find the derivative of f(x) = 3x^2(x + 5).
- 6
Find the derivative of f(x) = (x^2 + 1)(x^3 - 4).
- 7
Find the derivative of f(x) = (2x + 1)/(x - 3).
- 8
Find the derivative of f(x) = (x^2 + 4)/x.
- 9
Find the derivative of f(x) = (3x - 2)^4.
- 10
Find the derivative of f(x) = (x^2 + 5x)^3.
- 11
Find the derivative of f(x) = sqrt(x), written as x^(1/2).
- 12
Find the derivative of f(x) = 1/x^3, written as x^(-3).
- 13
A particle moves so that its position is s(t) = 2t^3 - 9t^2 + 12t. Find the velocity function v(t).
- 14
The cost function is C(x) = 5x^2 + 10x + 200. Find C'(x) and explain what it represents.
- 15
Find the derivative of f(x) = x^3 - 4x^2 + 7x - 6, then evaluate f'(2).