g(x)=sinx
(Cos u) u’
g(x)=cosx
(-sin u)u’
g(x)=tanx
(Sec^2 u)u’
g(x)=cotx
(-Csc^2 u)u’
g(x)=secx
(sec u tan u)u’
g(x)=cscx
(-csc u cot u)u’
h(x)=sin^-1 x
(1/sqrt(1-u^2)) u’
h(x)=cos^-1x
-(1/sqrt(1-u^2)) u’
h(x)=tan^-1x
(1/(1+u^2))u’
h(x)=cot^-1x
-(1/(1+u^2))u’
h(x)=sec^-1x
(1/(u sqrt(u^2-1)))u’
h(x)=csc^-1x
-(1/(u sqrt(u^2-1)))u’
f(x)= e^x
(e^u)u’
f(x)=a^x
a^u (ln a)u’
f(x)=lnx
(1/u)u’
g(x)= lul
(u/ lul )u’