a)
[tex]\frac{\partial f(x,y,z)}{\partial x}=\frac{1}{2\sqrt{x^2+y^2+z^2}}*\frac{\partial(x^2+y^2+z^2)}{\partial x}=\frac{2x}{2\sqrt{x^2+y^2+z^2}}=\frac{x}{\sqrt{x^2+y^2+z^2}}\\\\\frac{\partial f(x,y,z)}{\partial y}=\frac{1}{2\sqrt{x^2+y^2+z^2}}*\frac{\partial(x^2+y^2+z^2)}{\partial y}=\frac{2y}{2\sqrt{x^2+y^2+z^2}}=\frac{y}{\sqrt{x^2+y^2+z^2}}\\\\\frac{\partial f(x,y,z)}{\partial z}=\frac{1}{2\sqrt{x^2+y^2+z^2}}*\frac{\partial(x^2+y^2+z^2)}{\partial z}=\frac{2z}{2\sqrt{x^2+y^2+z^2}}=\frac{z}{\sqrt{x^2+y^2+z^2}}[/tex]
b)
[tex]\frac{\partial f(x,y)}{\partial x}=e^y*\frac{\partial e^x}{\partial x}=e^y*e^x\\\\\frac{\partial f(x,y)}{\partial y}=e^x*\frac{\partial e^y}{\partial y}=e^x*e^y[/tex]
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