I have to find ∂z/∂x and dz/dx if z=ln(e^x+e^y) ,y=x^3 Awesome.Now, I write ∂z/∂x=(∂z/∂y)*(∂y/∂x) .I find ∂z/∂y=e^y/(e^x+e^y) ..but how do I find ∂y/∂x? what is its value?
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Is this the whole question? And can you edit your first line, you ask the same twice? – Bob Apr 20 '13 at 12:09
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1Go to the FAQ section to read about how to use LaTeX in this site to write mathematics properly – DonAntonio Apr 20 '13 at 13:53
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Assuming you didn't show the entire question yet, I think you want to know this:
The derivative of $z$ with respect to $x$: $$\frac{\partial z}{\partial x}=\frac{e^x}{e^x+e^y}$$
The derivative of $z$ with respect to $y$: $$\frac{\partial z}{\partial y}=\frac{e^y}{e^x+e^y}$$
The derivative of $y$ with respect to $x$: $$\frac{\partial y}{\partial x}=3x^2$$
Your approach won't work on different formulas. As you can see when you multiply the partial derivatives you suggested.
Bob
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