Derivative rules/Integration rules

d/dx e^x

e^x

d/dx a^x

A^x lna

d/dx e^g(x)

e^g(x) * g’(x)

d/dx a^g(x)

ln(a) * a^g(x) * g’(x)

d/dx lnx

1/x

d/dx ln(g(x))

g’(x)/g(x)

d/dx sinx

cosx du/dx

d/dx cosx

-sinx du/dx

d/dx tanx

sec²x du/dx

d/dx cscx

-cscxcotx du/dx

d/dx secx

secxtanx du/dx

d/dx cotx

-csc²x du/dx

d/dx sin^-1 x

1/rad(1-x²) du/dx

d/dx cos^-1x

-1/rad(1-x²) du/dx

d/dx tan^-1x

1/(1+x²) du/dx

d/dx cot^-1x

-1/(1+x²) du/dx

d/dx sec^-1x

1/abs x rad(x²-1) du/dx

d/dx csc^-1x

-1/abs x rad(x²-1) du/dx

int k dx

kx+c

int x^a dx

x^a+1/a+1 +c

int 1/x dx OR int x^-1 dx

ln abs x + c

int a^x dx

a^x/lna + c

int e^x dx

e^x + c

int cosx dx

sinx + c

int sinx dx

-cosx + c

int sec²x dx

tanx + c

int secxtanx dx

secx + c

int csc²x dx

-cotx + c

int cscxcotx dx

-cscx + c

int kf(x) dx

k int f(x)dx

int [f(x)±g(x) dx

int f(x)dx ± int g(x)dx