AP Calc AB: Derivatives & Antiderivatives to Know

f’(x)sinx

cosx

f’(x)tanx

sec²x

f’(x)secx

(secx)(tanx)

f’(x)cosx

-sinx

f’(x)cotx

-csc²x

f’(x)cscx

-cscx(cotx)

(cos²x) + (sin²x)

1

f’(e^x)

e^x

f’(lnx)

1/x @ x>0

f’(a^x)

a^x * ln(a)

f’(log_ax)

1/[x * ln(a)]

f’(sin^-1x)

1/[sqrt(1-x²)]

f’(tan^-1x)

1/(1+x²)

f’(sec^-1x)

1/[|x|(sqrt x²-1)]

f’(cos^-1x)

-1/sqrt(1-x²)

f’(cot^-1x)

-1/(1+x²)

f’(csc^-1x)

-1/[|x|(sqrt x²-1)]

∫cosx)dx

Sin(x)+c

∫(sinx)dx

-cos(x)+c

∫(sec²x)dx

tan(x)+c

∫(secx • tanx)dx

sec(x)+c

∫(cscx •cotx)dx

-csc(x)+c

∫(csc²x)dx

-cot(x)+c