Tables of Derivatives

A table of the first derivatives of common functions and used in calculus is presented.

f(x) d [f(x)] / dx
x n n x n - 1
e x e x
ln (x) 1 / x
sin x cos x
cos x - sin x
tan x sec 2x
cot x - csc 2x
sec x sec x tan x
csc x - csc x cot x
arcsin x 1 / sqrt (1 - x 2)
arccos x - 1 / sqrt (1 - x 2)
arctan x 1 / (1 + x 2)
sinh x cosh x
cosh x sinh x
tanh x sech 2 x
coth x - csch 2 x
sech x - sech x tanh x
csch x - csch x coth x
arcsinh x 1 / sqrt [x 2 + 1 ]
arccosh x 1 / sqrt [x 2 - 1 ]
arctanh x 1 / [ 1 - x 2 ]

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