Calculus—Derivatives to Memorize

f(x)=e^u

f’(x)=e^u×du

f(x)=a^u

f’(x)=a^u×ln(a)×du

f(x)=sin(u)

f’(x)=cos(u)×du

f(x)=tan(u)

f’(x)=sec²(u)×du

f(x)=sec(u)

f’(x)=sec(u)×tan(u)×du

f(x)=ln(u)

f’(x)=1/u×du OR du/u

f(x)=loga(u)

f’(x)=1/u×ln(a)×du OR du/u×ln(a)

f(x)=cos(u)

f’(x)=-sin(u)×du

f(x)=cot(u)

f’(x)=-csc²(u)×du

f(x)=csc(u)

f’(x)=-csc(u)×cot(u)×du

arcsin(x)/sin⁻¹(x)

1/√1-x²

arccos(x)/cos⁻¹(x)

-1/√1-x²

arcsec(x)/sec⁻¹(x)

1/|x|√x²-1

arccsc(x)/csc⁻¹(x)

-1/|x|√x²-1

arctan(x)/tan⁻¹(x)

1/1+x²

arccot(x)/cot⁻¹(x)

-1/1+x²