Question

求复合函数的导数y=Sin^3 2x^3表示3次方y'=3sin^2 2x * sin^2 2x' =3sin^2 2x

Answer 1

y'=3sin^2 2x * sin^2 2x'

这一步就不对

y=u^3,u=sinv,v=2x

所以y'=3u^2*u'=3sin^2 2x*(sinv)'

=3sin^2 2x*cosv*v'

=3sin^2 2x*cos2x*(2x)'

=2*3sin^2 2x*cos2x

=3*sin2x*(2sin2x*cos2x)

=3sin2xsin4x