设曲线f(x)在(0,1)上可导,且y=f(Sin2(2为上标)x)f(cos2(2为上标)x),求Dy/Dx

问题描述:

设曲线f(x)在(0,1)上可导,且y=f(Sin2(2为上标)x)f(cos2(2为上标)x),求Dy/Dx

y=2*sinx*cosx*f'(sin^2x)f(cos^2x)-2*sinx*cosx*f'(cos^2x)f(sin^2x)

y=f(sin^2x)f(cos^2x)
= f‘(sin^2x)f(cos^2x)+f(sin^2x)f’(cos^2x)
=2*sinx*cosx*f'(sin^2x)f(cos^2x)-2*sinx*cosx*f'(cos^2x)f(sin^2x)