设z=f(x,y)=arctanx/y ,y=√(x^2+1) ,求dz/dx
问题描述：
设z=f(x,y)=arctanx/y ,y=√(x^2+1) ,求dz/dx
答
z'=1/[1+(x/y)²]* (x/y)'=1/[1+(x/y)²] *(y-xy')/y²=(y-xy')/(y²+x²)而y'=1/[2√(x²+1)]*2x=x/√(x²+1)所以z'=[√(x²+1)-x²/√(x²+1)]/(x²+1+x²)=1/[(...