Calculus Cheat Sheet

Calculus Cheat Sheet (u=u(x); v=v(x); a, n are constants) Derivatives: d a0 dx d x 1 dx d d au  a u dx dx d n x  nx n 1 dx d n d u  nu n 1 u dx dx d u d e  eu u dx dx d 1 d ln u  u dx u dx d d cosu   sin u u dx dx d d sin u  cosu u dx dx d d d (u  v)  u  v dx dx dx d d d (uv)  v u  u v dx dx dx d u 1 d 1 d u 2 v   dx  v  v dx v dx Integrals: a f ( x)dx  a  f ( x)dx  a dx  ax 1  (u  v)dx   udx   vdx e 1 ax e a x n 1  x dx  n  1 (except for n  1) n  x dx  ln x 1 ax dx   sin axdx   a cos ax  f ( x)dx  y(b)  y(a) a b 1  cos axdx  a sin ax wherey(x)   f ( x)dx