y是一個復(fù)合函數(shù).
設(shè)：f(x)=x+√x
代入所給函數(shù),有：y=cos[f(x)]
f'(x)=1-1/√x=1-x^(-1/2)=(x-√x)/x
f''(x)=(1/2)x^(3/2)=(1/2)√(x^3)
y'={-sin[f(x)]}×f'(x)
y''={-sin[f(x)]}'×f'(x)+{-sin[f(x)]}×f''(x)
={-cos[f(x)]}×[(x-√x)/x]-{sin[f(x)]}×[(1/2)√(x^3)]
=-[(x-√x)/x]×cos(x+√x)-[(1/2)√(x^3)]×sin(x+√x)