Calculus Cheat Sheet
(u=u(x); v=v(x); a, n are constants) Derivatives:
d a0 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