so I have two functions: $f(x,y) = (x^2,xy^2)$ and $y(u,v) = uv$. I need to calculate the $\frac{\partial y\circ f}{\partial x}(x,y)$.
Right now I am trying to understand how the partial derivatives of composite function works, but I don't have any example in my book. So I was wondering if you cold help me with the solution for this one to have it as an example so that I will be able to solve other exercises of this kind.
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Raducu Mihai
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2It cannot be $y\circ f$ because $y$ takes two arguments and $f(x,y)$ is one number so $y(f(x,y))$ doesn’t make sense – marwalix Jan 30 '20 at 08:35
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Ok so now I've edited the question. Sorry for this. – Raducu Mihai Jan 30 '20 at 09:02
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$y \circ f$ is a function in $x, y$, after which you can apply the chain rule. Another example is found here. – mi.f.zh Jan 30 '20 at 09:29
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Let’s do it the brutal way
$$y\circ f(x,y)=x^2\cdot xy^2=x^3y^2$$
And so
$${\partial(y\circ f)\over \partial x}(x,y)=3x^2y^2$$
marwalix
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