anonymous
  • anonymous
partial derivative (just the y part is asked for) sqrt(x-y)
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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anonymous
  • anonymous
\[df/dy \sqrt{x-y}\]
anonymous
  • anonymous
Treat x as a constant and differentiate as normal.
anonymous
  • anonymous
And the proper notation is: \[\frac{\partial f}{\partial y} = \frac{\partial}{\partial y} \sqrt{x - y}\]

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anonymous
  • anonymous
-1/2 (x-y)^-1/2 ?? seems like it should be harder than that
anonymous
  • anonymous
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.
anonymous
  • anonymous
that should have a: \[\lim_{h \rightarrow 0}\] /facepalm
anonymous
  • anonymous
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
anonymous
  • anonymous
Well I can give you one :P http://www.wolframalpha.com/input/?i=d%2Fdy+%28sqrt%28x-y%29%29
anonymous
  • anonymous
sure wolf knows but he never explains why =)
anonymous
  • anonymous
But if you understand sqrt(xy) I feel like sqrt(x - y) should be easier :P

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