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Find the first order partial derivatives of the function x = f(x,y) at the point (4,3) where:

[tex]f(x,y)=ln|(x+√(x^2+y^2))/(x-√(x^2+y^2))|[/tex]

I understand the method of partial derivatives and implementing the given point values once the partial derivatives are found, however I am having trouble trying to simplify the equation so that the partial derivatives can be found.

I have used the log rule to simplify the function but I think it can be simplified further but am stuck. So far Ive got:

[tex]In(x+√(x^2+y^2)-In(x-√(x^2-y^2)[/tex]

Do I then multiply out the In by whats in the brackets? Cause that doesnt look right when I work through the problem. Looking at similar problems I am guessing the equation being simplified would be

[tex] f(x,y) =x+√(x^2+y^2) [/tex]

but how do I get there?

[tex]f(x,y)=ln|(x+√(x^2+y^2))/(x-√(x^2+y^2))|[/tex]

I understand the method of partial derivatives and implementing the given point values once the partial derivatives are found, however I am having trouble trying to simplify the equation so that the partial derivatives can be found.

I have used the log rule to simplify the function but I think it can be simplified further but am stuck. So far Ive got:

[tex]In(x+√(x^2+y^2)-In(x-√(x^2-y^2)[/tex]

Do I then multiply out the In by whats in the brackets? Cause that doesnt look right when I work through the problem. Looking at similar problems I am guessing the equation being simplified would be

[tex] f(x,y) =x+√(x^2+y^2) [/tex]

but how do I get there?

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