高数多元函数偏导 若f(x,x^2)=x^4+2x^3+x,f1'(x,x^2)=2x^2-2x+1,则f2'(x,x^2)=
问题描述：
高数多元函数偏导 若f(x,x^2)=x^4+2x^3+x,f1'(x,x^2)=2x^2-2x+1,则f2'(x,x^2)=
答
取全微分.df(x,y)=f1'(x,y)dx+f2'(x,y)dy.
两边除以dx.有d(f(x,x^2))/dx=f1'(x,x^2)+f2'(x,x^2)*dy/dx
则4x^3+6x^2+1=2x^2-2x+1+f2'(x,x^2)*2x
f2'(x,x^2)=2x^2+2x+1