Differentiation Rules
In the rules below, f and g are differentiable functions and c is some constant.
•
d
(c) = 0
dx
•
d
(sec x) = sec x tan x
dx
•
d
c f (x) = c f 0 (x)
dx
•
d
(csc x) = − csc x cot x
dx
•
d
f (x) + g(x) = f 0 (x) + g0 (x)
dx
•
d −1 1
sin x = √
dx
1 − x2
•
d
f (x) − g(x) = f 0 (x) − g0 (x)
dx
•
d −1 1
cos x = − √
dx
1 − x2
•
d
f (x)g(x) = f 0 (x)g(x) + f (x)g0 (x)
dx
•
d −1 1
tan x =
dx
1 + x2
•
1
d −1 cot x = −
dx
1 + x2
!
f 0 (x)g(x) − f (x)g0 (x)
d f (x)
•
=
dx g(x)
(g(x))2
•
d n
(x ) = nxn−1
dx
•
d −1 1
sec x =
√
dx
|x| x2 − 1
•
d
f (g(x)) = f 0 (g(x))g0 (x)
dx
•
1
d −1 csc x = − √
dx
|x| x2 − 1
•
d
(sin x) = cos x
dx
•
d x
(e ) = ex
dx
•
d
(cos x) = − sin x
dx
•
d x
(b ) = bx ln b
dx
•
d
(tan x) = sec2 x
dx
•
d
1
(ln |x|) =
dx
x
•
d
(cot x) = − csc2 x
dx
•
d 1
logb |x| =
dx
x ln b