高数题：y^2f(x)+xf(y)=x^2(^代表平方),f(x)可微,求dy.

设函数y=y(x)由方程y^2 f(x)+xf(x)=x^2确定,其中f(x)为可微函数,求dy. 设y=y(x)是由方程y^2f(x)+xf(y)=x^2确定,其中f(x)是x的可微函数,试求dy/dx. 设f x 为可导函数,y=f^2(x+arctanx),求dy/dx y=f[(x-1)/(x+1)],f'(x)=arctanx^2,求dy/dx,dy f(xy)=xf(y)+yf(x) 求f(x) 设f(x)可导,且f'(0=1,又y=f(x^2+sin^2x)+f(arctanx),求dy/dx /x=0 设F(x)可导,y=f(x^2),则dy/dx=? 设f(x)为可导函数,求dy/dx (1)y=f(tanx) (2)y=f(x^2)+lnf(x) 设y=f(sinx)+e^x^2,f'(x)存在,求y'及dy 设f(u)可导,函数y=y(x)由x^y+y^x=f(x^2+y^2)所确定,则dy= 设f(x)可导,且y=f(x²)+f[f(x)],求dy/dx 设f(x)可导,求dy/dx y=sin f(x²)