画工大望院 d (logo x)=dx d(nx)=dx xina d(arcsin x) dx d(arccos x 2 arctan) d x d(arc cot x) 1+x 1+x2 2函数和、差、积、商的微分法则 d(u土y)=±h d( cu =cdu u vdu-udv d(uv =vdu+ udy 3.复合函数的微分法则 y=f|o(x)则l=叽lp(x)=yh=f(m)(x)d江西理工大学理学院 2. 函数和、差、积、商的微分法则 dx x a d x a ln1 (log ) = dx x d x 1 (ln ) = dx x d x 2 1 1 (arcsin ) − = dx x d x 2 1 1 (arccos ) − = − dx x d x 2 1 1 (arctan ) + = dx x d arc x 2 1 1 ( cot ) + = − d(u ± v) = du ± dv d(Cu) = Cdu d(uv) = vdu + udv 2 ( ) v vdu udv vu d − = 3. 复合函数的微分法则 y f x dy df x y dx f u x dx x = [ϕ( )]则 = [ϕ( )] = ′ = ′( )ϕ′( )