Differentiation Formulas
The following table provides the differentiation formulas for common functions. The first six rows correspond to general rules (such as the addition rule or the product rule) whereas the remaining rows contain the formulas for specific functions.
	F(x)	F'(x)
Addition	f(x) ± 9{x)	/'(*) ± sf(x)
Linearity	a f{x)	af'ix)
Product Rule	f(x)g(x)	f(x)g(x) + f(x)g'(x)
Quotient Rule	/(*)	f(x)g(x)-f(x)g'(x)
Chain Rule	/(»(*))	f(g(x)) ■ g'(x)
		f'(f-Hx))
Basic functions	xn      for any real n	nxn~x
	ex	ex
	or      (a > 0)	(In a)ax
	In a:	i X
Trig functions	sinx	cosx
	cosx	— sin a;
	tana;	—V- = 1 + tan2 x COS X
	arctanx = tan-1 x	1 1+x2
	arcsin x = sin-1 x	1 Vl-x2
Hyperbolic Trig	sinh a;	cosh a;
	cosh IE	sinh a;
	tanh x	i cosh2 x
	sinh-1 x	1 Vl+x2
	tanh-1x	1 1-x2