Partial Differentiation help

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SUMMARY

The discussion focuses on calculating the first partial derivatives of the function z = e^(uv), where u = x - y and v = xy. The user derived the partial derivatives as ∂w/∂x = (2xy - y²)e^[(x - y)(xy)] and ∂w/∂y = (x² - 2xy)e^[(x - y)(xy)]. Other participants confirmed the correctness of these derivatives, emphasizing the application of the chain rule in the differentiation process.

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Partial Differentiation help please!

Hi, I was wondering if anyone is doing degree level maths who can help me with the following question. Thanks very much!

I was asked to find the first partial derivatives of z (in terms of x and y) with respect to x and y where:

z = e^(uv) where u = x -y and v = xy

The answer I got was:

∂w/∂x = (2xy-y²) e^[(x-y)(xy)]

and ∂w/∂y = (x² - 2xy) e^[(x-y)(xy)]

Can anyone help me confirm if that is right? I've used a particular chain rule i was given in my notes to approach the answer. Thanks again
 
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