Re: How do u go about doing this---?
- To: mathgroup@smc.vnet.net
- Subject: [mg10961] Re: [mg10844] How do u go about doing this---?
- From: Robert Pratt <rpratt@math.unc.edu>
- Date: Sat, 14 Feb 1998 00:53:32 -0500
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. > > > >