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