MATH 152 Exam 2

d/dx (x^n)

nx^n-1 (power rule)

d/dx (lnx)

1/x

d/dx ln(g(x))

g'(x)/g(x)

d/dx(e^x)

e^x

d/dx (a^x)

a^x ln(a)

d/dx e^g(x)

g'(x)e^g(x)

a^g(x)

ln(a)a^g(x)g'(x)

d/dx cos^-1(x) (arccosx)

-1/√(1-x^2)

d/dx sin^-1(x) (arcsinx)

1/√(1-x^2)

d/dx tan^-1(x) (arctanx)

1/(1+x^2)

d/dx sinx

cosx

d/dx cosx

-sinx

d/dx tanx

sec^2x

d/dx secx

secxtanx

d/dx cscx

-cscxcotx

d/dx cotx

-csc^2x

d/dx secx

secxtanx

product rule

uv' + vu'

quotient rule

(uv'-vu')/v²

chain rule

f'(g(x))g'(x)

integral (x^n)

x^n+1/n+1 +C

integral of e^x

e^x + C

integral a^x

a^x/ lna + C

Integral of 1/x

ln|x| +C

integral of 1/(x^2+a^2)

(1/a)arctan(x/a)+C

integral of 1/1+x^2

arctanx + C

integral of 1/sqrt(1-x^2)

arcsinx+C

integral of cosx

sinx +C

integral of sinx

-cosx +C

integral of secxtanx

secx + c

integral of sec^2x

tanx + C

integral of cscxcotx

-cscx +C

integral of csc^2x

-cotx + c

Log rule lnPQ

LnP + LnQ

Log rule LnP/Q

Lnp- lnq

LnP^r

= rlnP

Useful trig identities (6)

cos^2x+sin^2x=1

1+tan^2(x)=sec^2(x)

cos^2(x) = 1/2(1+cos(2x))

sin^2(x) = 1/2(1-cos(2x))

sin(2x) = 2sin(x)cos(x)

cos(2x) = 1-2sin^2x = 2cos^2x-1