题目

y=sin³（3x+π/4）的导数

提问时间：2020-08-02

答案

令3x+π/4=t
(sin^3t)'=((sin^2t)(sint))'
利用求导乘法法则
=（sin^2t)'sint+(sint)'sin^2t
对sin^2t再利用求导法则,得到
=(sint(sint)'+(sint)'sint)sint+costsin^2t
=(2sintcost)sint+costsin^2t
=2sin^2tcost+costsin^2t
=3costsin^2t
带入t=3x+π/4
=3cos(3x+π/4)sin^2(3x+π/4)