Calculus Derivatives

Basic Derivatives

100

What is the derivative of

 y = 3x² ?

y' = 6x

200

Find the derivative of

 f(x) = ln6

f'(x)=0

300

Find the derivative of

 f(x) = 6x³ + x - 2

f'(x)=18x² + 1

400

Find the derivative of

 f(x) = 3sinx - 2cosx

f'(x)=3cosx + 2sinx

500

Find and SIMPLIFY f'(x):

f(x)=(3+x³-xe)/x

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

Product and Quotient Rule (and some mixed)

100

Find the derivative of

 y = 3x² sin x

y'=3x² cos x + 6x sin x

200

Find the derivative

f(x) = (3x - 2x²)(5 + 4x)

Do not simplify

f'(x)=(3x-2x²)(4)+(3-4x)4

300

Find the derivative of 

y = sin(5x )/(x² + 1)

Do not Simplify

y'=[(x²+1)cos(5x)5-sin(5x)2x]/(x²+1)²

400

Find the derivative of 

f(x) = (e^2xsin(x))/x⁴

f'(x)=[x⁴(e^2xcosx+2e^2xsinx)-e^2xsin(x)4x³]/(x⁴)²

500

The derivative of 

y=(x³+7)(e^x)

y'= 3x²e^x + e^x(x³+7)

Trigonometric Derivatives

100

Find the derivative

f(x) = sec x

f'(x) = sec x tan x

200

Find the derivative

y = csc(x)tan(x)

y' = sec x tan x

300

Find the derivative

 f(x) = sin x tan x

f'(x) = cos x tan x + sec²x sin x

400

Find the derivative of

 y = tan x tan x 

y' = 2 sec² x tan x 

500

Find the derivative of 

y=sin x (3e^x)

y'= cos x (3e^x ) + (3e^x) sin x 

Miscellaneous

100

Find y''' if 

y = e^x

y''' = e^x

200

What is the limit definition of a derivative? 

lim as h -> 0 of ( f(x + h) - f(x) ) / h 

300

Who is considered the English "Father of Calculus"?

Sir Isaac Newton

400

Who is considered the French "Father of Calculus"? 

Wilhelm Gottfried Leibniz 

500

What is the triple derivative of y = cos(x) ? 

y''' = sin x