作业帮设y=f[(sinx)^2]+f[(cosx)^2],f(x)可微,求dy
来源：学生作业帮助网 编辑：作业帮 时间：2024/04/28 19:06:37
![设y=f[(sinx)^2]+f[(cosx)^2],f(x)可微,求dy](/uploads/image/z/7077941-53-1.jpg?t=%E8%AE%BEy%3Df%5B%28sinx%29%5E2%5D%2Bf%5B%28cosx%29%5E2%5D%2Cf%28x%29%E5%8F%AF%E5%BE%AE%2C%E6%B1%82dy)
设y=f[(sinx)^2]+f[(cosx)^2],f(x)可微,求dy
设y=f[(sinx)^2]+f[(cosx)^2],f(x)可微,求dy
设y=f[(sinx)^2]+f[(cosx)^2],f(x)可微,求dy
dy=f'(sinx)^2]d(sinx)^2+f'(cosx)^2]d(cosx)^2
=2sinxf'(sinx)^2]d(sinx)+2cosxf'(cosx)^2]d(cosx)
=2sinxcosxf'(sinx)^2]dx+2cosx(-sinx)f'(cosx)^2dx
=[sin2xf'(sinx)^2-sin2xf'(cosx)^2]dx
dy＝{sin2x* [f'(sinx^2)-f'(cosx^2)]}dx
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