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解ï¼è®¾z=f(xï¼u)ï¼u=x/yï¼å
∂z/∂x=∂f/∂x+(∂f/∂u)(∂u/∂x)=∂f/∂x+(1/y)(∂f/∂u)
∂z/∂y=(∂f/∂u)(∂u/∂y)=-(x/y²)(∂f/∂u)
∂²z/∂x²=∂²f/∂x²+(1/y)(∂²f/∂u²)(∂u/∂x)=∂²f/∂x²+(1/y²)(∂²f/∂u²)
∂²z/∂y²=(2x/y³)(∂f/∂u)-(x/y²)(∂²f/∂u²)(∂u/∂y)=(2x/y³)(∂f/∂u)+(x/y⁴)(∂²f/∂u²)
∂²z/∂x∂y=-(1/y²)(∂f/∂u)+(1/y)(∂²f/∂u²)(∂u/∂y)=-(1/y²)(∂f/∂u)-(x/y³)(∂²f/∂u²).
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