Calculus Derivatives - Version 2

Basic Derivatives

100

What is the derivative of

y = 3x^2

 ?

y' = 6x

200

Find the derivative of 

f(x) = 5

0

300

Find the derivative of 

f(x) = 6x^3 + x - 2

18x² + 1

400

(x)=5x^3 +2x, h'(2)= ? 

62

500

Find the third derivative of 

5x^5+2x^2+4x

300x^2

Product and Quotient Rule

100

Find the derivative of 

y = 3x^2 sin x

3x^2 cos x + 6x sin x

200

f(x) = (3x - 2x^2)(5 + 4x)

-24x^2 + 4x + 15

300

Find the derivative of 

y = (5x - 2)/(x^2 + 1)

(-5x^2 + 4x + 5)/(x^2 + 1)^2

400

Find the derivative of 

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

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

500

Find the Derivative of 

y= (2x+1)/(2x-1)

y'=-4/(2x-1)^2

Logarithms

100

Find y' if

y = log_2x

y = 1/(xln2)

200

Find the derivative of 

f(x) = 4log_3x

4/(xln3)

300

Find y' if 

y = 2log₄x + log₈x

Y'=2/(xln4) + 1/(xln8)

400

f(x) = 3log_5x + 7log_5x

Find f'(x)

f'(x) = 10/(xln5)

500

f(x) = 11log_9x - 9log_9x

Find f'(x)

f(x) = 2/(xln9)

Trigonometric Differentiation

100

Find the derivative of

f(x) = 3sinx - 2cosx

3cosx + 2sinx

200

y=4sinx - 5cosx

y'= 4cosx +5sinx

300

The derivative at

y= 2 sin x,  at   x=pi/2

y'= - 2

400

The derivative of

y= 3cosx,  at   x=pi/2

y= 0

500

y= 7cosx - 2sinx, at  x=pi

y'= 2

Natural Logarithms and Exponentials

100

3lnx

3/x

200

y=-4e^(x)

y=-4e^(x)

300

f(x)=3x^3 - 7e^(x)

f(x)=9X^2 - 7e^(x)

400

y=6ln(x) + 8e^x + e^2

y=6/x + 8e^x

500

g(x)=4xlnx

4+4lnx