Question

假设U=F(G(X)+Y),其中Y=Y(X)由方程Y方+e 的y方＝SIN（X＋Y）确定,而且F,G一阶可导,求du/d

Answer 1

du/dx =F(G(X)+Y)'*(G(X)'+Y')

由y^2＝SIN（X＋Y）,得 2ydy=cos(x+y)*(dx+dy)

所以 dy/dx=cos(x+y)/[2y-cos(x+y)]

所以du/dx =F(G(X)+Y)'*(G(X)'+cos(x+y)/[2y-cos(x+y)])