AP Calc AB Derivative Formulas

d/dx [c] =

0

d/dx [x] =

1

d/dx [cx] =

c

d/dx [u + v] =

u’ + v’

d/dx [xⁿ] =

nx^n-1

d/dx [uv] =

uv’ + vu’

d/dx [u/v] =

(vu' - uv')/v²

d/dx [f(u)] =

f’(u)u’

d/dx [e^x] =

e^x

d/dx [lnx] =

1/x

d/dx [log_ax] =

1/(lna)x

d/dx [a^x] =

(lna)a^x

d/dx [sinx] =

cosx

d/dx [cosx] =

-sinx

d/dx [tanx] =

sec²x

d/dx [cotx] =

-csc²x

d/dx [secx] =

secxtanx

d/dx [cscx] =

-cscxcotx

d/dx [arcsinx] =

1/sqrt(1-x²)

d/dx [arccosx] =

-1/sqrt(1-x²)

d/dx [arctanx] =

1/(1+x²)

d/dx [arccotx] =

-1/(1+x²)

d/dx [arcsecx] =

1/|x|sqrt(x²-1)

d/dx [arccscx] =

-1/|x|sqrt(x²-1)