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MathGroup Archive 1998

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Re: How do u go about doing this---?



I assume you mean that the function is f(x,y) since you want to
differentiate with respect to y.

To do the problem by hand, just use the quotient rule to compute the two
partial derivatives separately.  Then square each one and add them up.
You will probably need to use some trig identities (e.g. double-angle
formulas) to simplify your answer so that it appears as below.

To do the problem using Mathematica, you could do:

f[x_,y_]:=(Sin[x]+Cos[y])/(Sin[x]-Cos[y])

Simplify[D[f[x,y],x]^2+D[f[x,y],y]^2]

Rob Pratt
Department of Mathematics
The University of North Carolina at Chapel Hill CB# 3250, 331 Phillips
Hall
Chapel Hill, NC  27599-3250

rpratt@math.unc.edu

http://www.math.unc.edu/Grads/rpratt/

On Tue, 10 Feb 1998, McAllister wrote:

> 
> Let f(x) = sin(x)+cos(y)
>                 -----------------
>                 sin(x) - cos(y)
> 
> Show that
>                 (df/dx)^2 + (df/dy)^2    =
> 
>                 2+cos(2(x-y))+cos(2(x+y))
>                 -----------------------------------
>                             (sin(x)-cos(y))^4
> 
> 
> Thanks,
> 
> L.
> 
> 
> 
> 




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