I cannot figure out how to do this problem completely:(adsbygoogle = window.adsbygoogle || []).push({});

If U =x^{3}y, find [itex]\frac{dU}{dt}[/itex] if x^{5}+ y = t and x^{2}+ y^{3}= t^{2}.

I know that I am using the chain rule here and I have the partial derivates of U:

[itex]\frac{∂U}{∂x}[/itex] = 3x^{2}y

[itex]\frac{∂U}{∂y}[/itex] = x^{3}

So far I have the equation given below.

[itex]\frac{dU}{dt}[/itex] = 3x^{2}y [itex]\frac{dx}{dt}[/itex] + x^{3}[itex]\frac{dy}{dt}[/itex]

However, I do not know how to calculate [itex]\frac{dx}{dt}[/itex] and [itex]\frac{dy}{dt}[/itex]. I tried to calculate them implicitly but I am still working with three variables x, y, and t. Could you please help me with this? Any insight would be greatly appreciated! Thank you!

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# Differentials of Composite Functions

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