Math2.org Math Tables: Table of Derivatives

Power of x.

c = 0

x = 1

xn = n x(n-1)  Proof

Exponential / Logarithmic

ex = ex  Proof

bx = bx ln(b)  Proof

ln(x) = 1/x  Proof

Trigonometric

sin x = cos x  Proof	csc x = -csc x cot x  Proof
cos x = - sin x  Proof	sec x = sec x tan x  Proof
tan x = sec2 x  Proof	cot x = - csc2 x  Proof

Inverse Trigonometric

arcsin x  =  1  (1 - x2)	arccsc x =  -1  |x| (x2 - 1)
arccos x =   -1  (1 - x2)	arcsec x =  1  |x| (x2 - 1)
arctan x =  1  1 + x2	arccot x =  -1  1 + x2

Hyperbolic

sinh x = cosh x  Proof	csch x = - coth x csch x  Proof
cosh x = sinh x  Proof	sech x = - tanh x sech x  Proof
tanh x = 1 - tanh2 x  Proof	coth  x = 1 - coth2 x  Proof

 
 
Those with hyperlinks have proofs.