像y=sin{In(3+2x²)²}这种复合函数怎么求导,最好用wps作具体过程~

问题描述:

像y=sin{In(3+2x²)²}这种复合函数怎么求导,最好用wps作具体过程~

就是重复应用复合函数的求导公式:f(g(x))'=f'(x)g'(x)
y‘=sin{In(3+2x²)²}'
=cos(In(3+2x²)²) *{In(3+2x²)²}'
=cos(In(3+2x²)²) *1/(3+2x²)²*{ (3+2x²)² }'
=cos(In(3+2x²)²) *1/(3+2x²)²* 2(3+2x²)*(3+2x²) '
=cos(In(3+2x²)²) *1/(3+2x²)²* 2(3+2x²)*4x
=cos(In(3+2x²)²) *8x/(3+2x²)