设$ u(x)、v(x)$可导，则
四则求导法则四则求微分法则$$ (u\pm v)'=u'\pm v'$$$$d(u\pm v) = du\pm dv$$$$ (1)(uv)'=u'v+v'u\ (2)(ku)'=ku'(k为常数)\ (3)(uvw)'=u'vw+uv'w+uvw'$$$$(1)d(uv)=udv+vdu\ (2)d(ku)=kdu(k为常数)\ (3)d(uvw)=vwdu+uwdv+uvdw$$$$(\frac{u}{v})'=\frac{u'v-uv'}{v^2}$$$$d(\frac{u}{v})=\frac{vdu-udv}{v^2}$$复合函数求导法则-链式法则
设\(y=f(u)\)可导，\(u=\phi(x)\)可导，且\(\phi^{'}(x)\neq0\)，则\(y=f[\phi(x)]\)可导，且
\[\frac{dy}{dx}=\frac{dy}{du}.\frac{du}{dx} = f^{'}(u).\phi^{'}(x)= f^{'}[\phi(x)].\phi^{'}(x)\]反函数求导法则
\[(1)设y=f(x)可导且f^{'}(x)\neq0，又x=\phi(y)为其反函数，则x=\phi(y)可导，且\\\phi^{'}(y)=\frac{1}{f^{'}(x)}\\设y=f(x)二阶可导且f^{'}(x)\neq0，又x=\phi(y)为其反函数，则x=\phi(y)二阶可导，且\\\phi^{''}(y)=-\frac{f^{''}(x)}{f^{'3}(x)}\]