Question

partial derivative (just the y part is asked for) sqrt(x-y)

Answer 1

\[df/dy \sqrt{x-y}\]

Answer 2

Treat x as a constant and differentiate as normal.

Answer 3

And the proper notation is:
\[\frac{\partial f}{\partial y} = \frac{\partial}{\partial y} \sqrt{x - y}\]

Answer 4

-1/2 (x-y)^-1/2 ?? seems like it should be harder than that

Answer 5

That's right. And its that simple, just treat all the other variables as constant. For example, the derivative of a function of one variable is given as:
\[\frac{d f}{dx}=\lim_{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}\]
Notice we are varying x. As a function of multiple variables we have:
\[\frac{\partial f}{\partial x_i} = \frac{f(x_1,x_2,...,x_i + h, ..., x_n) - f(x_1,x_2,...,x_i,..,x_n)}{h}\]
Notice here that when we take a derivative with respect to x_i (say 'y') we only vary that variable and leave the others.

Answer 6

that should have a:
\[\lim_{h \rightarrow 0}\]
/facepalm

Answer 7

I just didn't like the x-y turning into -1 I guess -- seemed a little too glib. lots of solutions on the intertubes for sqrt(xy) but not so much x(+-)y thanks a ton

Answer 8

Well I can give you one :P
http://www.wolframalpha.com/input/?i=d%2Fdy+%28sqrt%28x-y%29%29

Answer 9

sure wolf knows but he never explains why =)

Answer 10

But if you understand sqrt(xy) I feel like sqrt(x - y) should be easier :P