Calc Unit 4

Inverse Trig Derivatives

100

What is the derivative of sin^-1(x)?

1/sqrt(1-x²)

200

What is the derivative of cos-1(x)?

-1/sqrt(1-x²)

300

What is the derivative of tan^-1(x)?

1/(1+x²)

400

What is the derivative of cot^-1(x)?

-1/(1+x²)

500

What is the derivative of sin^-1(5x³)?

15x²/sqrt(1-(5x³)²)

Derivative of ln

100

y=ln4x

What is y'= 1/x

200

y=ln(lnx)

What is y'= 1/(xlnx)

300

y=x+lnx²

What is y'= (x+2)/x

400

y=ln(sinx)

What is y'= cosx/sinx= cotx

500

y=ln(1+e^x)

What is y'=e^x/(1+e^x)

Derivative of e^x

100

y=e^2x

What is y'=2e^2x

200

y=e^-x

What is y'=-e^-x

300

y=e^(2x/3)

What is y'= (2/3)*e^(2x/3)

400

y=e^√x

What is y'= (1/(2√x))*e^√x

500

y=xe²-e^x

What is y'= e²-e^x

Chance with Derivatives!

100

y=ln(x²)

What is y'= 2/x

200

y=log₂(x²)

What is y'= 2/(xln2)

300

y=7^x + 4e^x

What is y'= 7^xln7 + 4e^x

400

y=lnx*log₂x

What is y'= (log₂x)/x + lnx/(xln2)

500

y=x^lnx

What is y'= lnx*x^(lnx-1)*(1/x)

L'Hopital's Rule

100

L'Hopital's Rule can only be applied with which two primary indeterminate forms?

0/0, oo/oo

200

Find the following limit: 

lim_(x -> 0) (3e^x-2e^(2x)-e^(3x))/(e^x+e^(2x)-2e^(3x))

4/3

300

Find the following limit: 

lim_(x ->-oo) (x^2)/(e^(-x))

0

400

Find the following limit:

lim_(x->oo) x^2/e^x

0

500

Find the following limit: 

lim_(x -> 1) (arctan(x)-(pi/4))/(x-1)

1/2