Calculus Derivatives

Basic Derivatives

100

What is the derivative of      

y = 3x² 

y' = 6x

200

Find the derivative of 

f(x) = 5

0

300

Find the derivative of 

f(x) = 6x³ + x - 2

18x² + 1

400

Find the derivative of 

f(x) = 3x - 2/x

3+2/x²

Product and Quotient Rule

100

Find the derivative of 

y = 3x²(x⁴-x)

18x⁵-9x²

200

f(x) = (3x - 2x²)(5 + 4x)

-24x² + 4x + 15

300

Find the derivative of 

y = (5x - 2)/(x² + 1)

(-5x² + 4x + 5)/(x² + 1)²

400

Find the derivative of 

f(x) = (2x + 5)/(x)^1/2

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

Chain Rule

100

Find y' if y = (3x - 9)⁴

12(3x - 9)³

200

Find the derivative of 

f(x) = (5x³+3)^-2

-30x²(5x³+3)^-3

300

Find y' if y = (9x² + 4)^1/3

(6x)/(9x² + 4)^2/3

400

f(x) = (-x⁴+6x³)² find f'(x)

2(-x⁴+6x³)(-4x³+18x²)

8x⁷-84x⁶+216x⁵

Implicit Differentiation

100

Find the derivative implicitly

x² + y² = 30

y' = - x/y

200

Find the derivative of x²+2y⁴=y³-5x

dy/dx = (-2x-5)/(8y³-3y²)

300

(y - 2)² = 4x - 12

y' = 2/(y - 2)

400

x³ - 3x²y + 2xy² = 12

y' = (-3x² + 6xy - 2y²)/(-3x² + 4xy)

Velocity and Slope

100

What is the slope of the tangent line of the function 

y=-7x+9

-7

200

What is the slope of the tangent line of the function

y=-4x²+8x - 3 at the point (2, -3)

-8

300

How long does it take for an object to hit the ground if it is dropped from 200 feet above the ground?  

3.5 seconds

400

An object is thrown with an initial velocity of -10 feet per second.  What is the velocity after 4 seconds?

-138 feet per second