Basic Derivatives
Product and Quotient Rule
Chain Rule
Equations of Tangent Lines
Chain Rule
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

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

What is f'(x) = 8x+20?

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 sin(x2) is...

What is f'(x) = 2xcos(x^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 first derivative of y=(2x+3)^2*(x+1)

What is f'(x) = 12x^2 + 32x +21?

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

Find the derivative of f(x) = x3tan(x2).

What is f'(x) = 3x^2tan(x^2) + 2x^4sec^2(x^2)

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'(pi/2) for sin(x^2)/tan(x)

What is -sin(pi^2/4)?

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