Practice applying the power rule, chain rule, product rule, and quotient rule to polynomial, radical, trigonometric, and rational functions.
Read each problem carefully. Show your work, identify the rule you use when helpful, and simplify your answer when possible.
Practice finding derivatives with the main differentiation rules
Math - Grade 9-12
- 1
Find d/dx of x^7.
- 2
Let f(x) = 5x^4 - 3x^2 + 7. Find f'(x).
- 3
Find the derivative of y = 4x^(-3) + sqrt(x).
- 4
Find the derivative of y = (3x^2 - 1)^5.
- 5
Find the derivative of y = sqrt(2x + 5).
- 6
Let y = (x^2 + 1)(x^3 - 4x). Find y' using the product rule.
- 7
Find the derivative of y = x^2 sin(x).
- 8
Let y = (2x + 1)/(x - 3). Find y' using the quotient rule.
- 9
Find the derivative of y = (x^2 + 4)/(3x^2 - 1).
- 10
Let y = (x^3 - 2x)^4. Find y' and then evaluate y' at x = 1.
- 11
Let y = (x^2 + 1)(3x - 2)^4. Find y'.
- 12
Find the derivative of y = (x^2 - 1)/(x^2 + 1).
- 13
Find the equation of the tangent line to f(x) = x^3 - 4x at x = 2.
- 14
A student says the derivative of y = (x^2 + 1)^3 is y' = 3(x^2 + 1)^2. Identify the mistake and give the correct derivative.
- 15
The position of an object is s(t) = t^4 - 2t^3 + t. Find the velocity v(t), the acceleration a(t), and their values at t = 2.