Question

设f(x)可导,求y=f(sin^2x)+f(cos^2x)的导数

Answer 1

y' = f'(sin^2x)f'(2x) + f'(cos^2x)f'(2x)
= 2(cos^2x) + 2(sin^2x)
= 2(cos^2x + sin^2x)

不确定你的式子是sin^2x 还是 sin^2(x), 按照前者算了下。

如果是后者，

y' = f'(sin^2 x)f'(x) + f'(cos^2 x)f'(x)
= cos^2(x) + sin^2(x)

Answer 2

y'=f'(sin²x)*(sin²x)'+f'(cos²x)*(cos²x)'
=f'(sin²x)*(2sinxcos)+f'(cos²x)*(-2cosxsinx)
=sin2x[f'(sin²x)-f'(cos²x)]