Mastering Technical Mathematics, Third Edition, 3rd Edition

Appendix 3

Table of Derivatives

 

 

Letters a, b, and c denote constants. Letters f, g, and h denote functions; m, n, and p denote integers; w, x, y, and z denote variables. The letter e represents the exponential constant (approximately 2.71828).

FUNCTION	DERIVATIVE
f (x) = a	f′(x) = 0
f (x) = ax	f′(x) = a
f (x) = axn	f′(x) = naxn-1
f (x) = 1/x	f′(x) = ln |x|
f (x) = ln x	f′(x) = 1/x
f (x) = ln g(x)	f′(x) = g-1(x) g′(x)
f (x) = 1/xa	f′(x) = − a / (xa+1)
f (x) = ex	f′(x) = ex
f (x) = ax	f′(x) = ax ln a
f (x) = ag(x)	f′(x) = [ag(x)] [g′(x)] (ln a)
f (x) = eax	f′(x) = aex
f (x) = eg(x)	f′(x) = [eg(x)] [g′(x)]
f (x) = sin x	f′(x) = cos x
f (x) = cos x	f′(x) = − sin x
f (x) = tan x	f′(x) = sec2 x
f (x) = csc x	f′(x) = −csc ...