设z=f(x,y)=arctanx/y ,y=√(x^2+1) ,求dz/dx答案是1/(x^2+y^2)*(√x^2+1)

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设z=f(x,y)=arctanx/y,y=√(x^2+1),求dz/dx答案是1/(x^2+y^2)*(√x^2+1)设z=f(x,y)=arctanx/y,y=√(x^2+1),求dz/dx答案是

设z=f(x,y)=arctanx/y ,y=√(x^2+1) ,求dz/dx答案是1/(x^2+y^2)*(√x^2+1)
设z=f(x,y)=arctanx/y ,y=√(x^2+1) ,求dz/dx
答案是1/(x^2+y^2)*(√x^2+1)

设z=f(x,y)=arctanx/y ,y=√(x^2+1) ,求dz/dx答案是1/(x^2+y^2)*(√x^2+1)
哦,刚才最后一步化简错了,更正一下:
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+y²)=1/[(x²+y²)√(x²+1)]