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Question: How to perform differentiation with respect to?

Hi,

I am trying to solve a differentiation but I think I am stuck since the solution is not what it should be.

So, I got the equation below

eq4 := `S__2 ` = sin(alpha - phi)*sin(-beta + alpha)*H^2*M/(2*sin(-beta - delta - phi + alpha)*sin(beta)*sin(alpha)) - S__1

And according to the paper I read, to get the maximum value of alpha for maximum value of S_2, I need to make differentiation to first derivative where dS_2/d(alpha) = 0

Then I should substitute back value of alpha to equation above and the paper shows that i should get equation below.

`S__2 ` = 1/2*M*K__a*H^2 - `S__2 `

where K_a is

`K__a`= [(sin(beta+phi))/((sin(beta))/(sqrt(sin(beta+delta))+(sqrt(sin(phi+delta)*(sin(phi-varepsilon)))/(sin(beta-varepsilon))))]

 

I know its really hard but hope someone can give some idea how to do it.

 

Thank you very much.

 

Kind regards

Faiz Farhan

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