Question

u=sin(x+y)+cos(x-y)

Answer 1

There is no question. :(

Answer 2

u=sin(x+y)+cos(x-y)=
=sinxcosy+sinycosx +cosxcosy+sinxsiny=
=sinx(siny+cosy)+cosx(siny+cosy)=
(siny+cosy)(sinx+cosx)

Answer 3

Oh, simplification! In which case @integralsabiti is right. :D

Answer 4

partial derrivative

Answer 5

With respect to what, \(x\) or \(y\)?

Answer 6

both

Answer 7

\[\frac{\partial u}{\partial x}=\cos\left(x+y\right)-\sin\left(x-y\right)\]\[\frac{\partial u}{\partial y}=\cos\left(x+y\right)+\sin\left(x-y\right)\]I know I didn't write out steps, but I'm not sure where you're confused.

Answer 8

You take the derivative of the entire equation with respect to one variable, pretending the other is constant.