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

0

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) = 4x3/2
What is 9/(4x5/2)?
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)/(2x3/2)
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) = 3x2/3 - 4x1/2 - 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?
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