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supaveggie
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Homework Statement
Trying to figure our how to solve the following: [itex]\frac{dW}{dσ}[/itex]
where [itex] W(σ) = 2π\int_0^∞y(H(x,σ))x,dx [/itex]
Homework Equations
both y and H(x,y) are continuous functions from 0 to Infinity
The Attempt at a Solution
Tried using the leibniz rule but it's not really getting me anywhere...
[itex]\frac{dW}{dσ} = 0+0+2π\int_0^∞\frac{\partial(y(H(x,σ))x)}{\partial \sigma},dx[/itex]
I'm not familiar with a chain rule for partial differentiation...
The solution I have is showing
[itex]\frac{dW}{dσ}= 2π\int_0^∞y'(H(x,σ))\frac{dH(x,σ)}{dσ}x,dx [/itex] I'm not understanding how they arrived at this.
It is also unclear what y' represents as ' is not necessarily used for derivative or defined anywhere...
Thanks
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