Calculus Derivatives

Basic Derivatives

Product and Quotient Rule

Chain Rule

Equations of Tangent Lines

Miscellaneous

100

What is the derivative of y = 3x² ?

y' = 6x

100

Find the derivative of y = 3x² sin x

3x² cos x + 6x sin x

100

Find y' if y = (3x - 9)⁴

12(3x - 9)³

100

The equation of the tangent line of f(x) = x² at x = 2

What is y = -4x - 4?

100

The points at which a function is not differentiable.

What is a sharp corner, a cusp, and a vertical tangent line?

200

Find the derivative of f(x) = 5

200

f(x) = (3x - 2x²)(5 + 4x)

-24x² + 4x + 15

200

Find the derivative of f(x) = sin 4x

4 cos 4x

200

The equation of the tangent line of f(x) = (x² + 2x)(x + 1) at x = 1

What is y - 6 = 11(x - 1)?

200

The derivative of f(x) = x³ + 2x using the limit definition of a derivative.

What is the limit as h approaches 0 of f(x+h) - f(x) divided by h , 3x² + 2?

300

Find the derivative of f(x) = 6x³ + x - 2

18x² + 1

300

Find the derivative of y = (5x - 2)/(x² + 1)

(-5x² + 4x + 5)/(x² + 1)²

300

Find y' if y = (9x² + 4)^1/3

(6x)/(9x² + 4)^2/3

300

The equation of the tangent line of f(x) = 1/∛(x² ) at x = 8

What is y - 1/4 = -1/36 (x - 8)?

300

The fourth derivative of f(x) = 4x^3/2

What is 9/(4x^5/2)?

400

Find the derivative of f(x) = 3sin x - 2cos x

3cos x + 2sin x

400

Find the derivative of f(x) = (2x + 5)/(x)^1/2

(2x - 5)/(2x^3/2)

400

Find f'(x) if f(x) = sin³ 4x

12 sin² 4x cos 4x

400

The point at which the function y = x + sin x on the interval 0 ≤ x ≤ 2π has a horizontal tangent line.

What is (π,π)?

400

Using the alternate form of the derivative, the derivative of f(x) = (x - 1)^2/3 at c = 1

What is DNE, the function is not differentiable at x = 1?

500

Find the derivative of f(x) = 3x^2/3 - 4x^1/2 - 2

What is (2/∛x) - (2/√x)?

500

Find the derivative of f(x) = (3 - (1/x))/(x + 5)

What is f'(x)=(-3x² + 2x + 5)/(x² + 5x)²?

500

Find the derivative of f(x) = sin ³ 4x

What is f'(x) = 12 sin² 4x cos 4x?

500

The point(s) at which f(x) = x⁴ - 3x² + 2 has a horizontal tangent line.

What is (0, 2), (√(3/2), -1/4), (-√(3/2), -1/4)?

500

Find f'(2) given that g(2) = 3, g'(2) = -2, h(2) = -1, and h'(2) = 4 when f(x) = g(x)/h(x)

What is -10?