Calculus Derivatives - No Trigonometry

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

 h(x)=f(x)*g(x), h'(3)= ? 

15-8pi

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)^²

18x+12

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

Chain Rule

100

Find y' if

y = (3x - 9)^4

12(3x - 9)^3

200

Find the derivative of 

f(x) = (4x^²- 1)^¹⁰

80x(4x^²-1)^⁹

300

Find y' if 

y = (9x^2 + 4)^(1/3)

(6x)/(9x^2 + 4)^(2/3

400

f(x) = sqrt(1-2x)

Find f'(x)

-(1-2x)^(-1/2)

500

Find 

f'(x)

f(x)=1/sqrt(x)

-1/(2sqrt(x^3))

Exponentials

100

e^x

e^x

200

y=2e^(sqrtx)

e^(sqrt(x))/sqrt(x)

300

f(x)=sqrt(5+e^(2x)

e^(2x)/sqrt(5+e^(2x)

400

y=3^(x^2-1)

2xln3(3^(x^2-1))

500

g(x)=(e^x+e^(-x))/x

[x(e^x-e^(-x))-(e^x+e^(-x))]/x^2

tangent lines &normal lines

100

what is the slope of the tangent line? the tangent line is 

5x-2.5=-2(y+3)

slope = 

-5/2

200

what is the normal line of 

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

y=1(x-3)+2.5

300

write the equation for the normal line to 

f(x)=(1+x)^(-1/2), x=3

y=16(x-3)+1/2

400

Write the equation for the tangent line when (2,1)

x^2y+y^2x=6

y'=5/8(x-2)+1

500

if 5x^2+2x^2y+y^2=8

 then y' at the point (1,1) is?

y'=-7/2