Partial Differentiation

FizzyCrow

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Joined
Nov 12, 2004
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I do not have a specific problem in mind, i just need to be told, in stupid terms hehehe, how to do a second partial differentiation. I know that there is the partial one with respect to x^2 and y^2, i an having problems understanding how you get the xy, yx one. I also know that they are, in my case, always equal. Any help is appreciated, if you need a problem, i can see if i can pull one from my book.


I also wanted to say thank you to everyone that helped me in my last posts, i've just been so busy, i have not been able to respond, so THANKS :)
 
f(x,y)=x2+y2\displaystyle f(x,y) = x^2 + y^2

fx\displaystyle f_x means the partial derivative of f(x,y) with respect to x. As you know, we treat y as a constant and differentiate wrt x:

fx=2x\displaystyle f_x = 2x
or fx=2x\displaystyle \frac{\partial f}{\partial x} = 2x

Likewise,
fy=2y\displaystyle f_y = 2y or fy=2y\displaystyle \frac{\partial f}{\partial y} = 2y

fxy\displaystyle f_{xy} reads from left to right in that: "the partial derivative of fx\displaystyle f_x wrt y".

But with the chain rule reads:

y(fx)\displaystyle \frac{\partial}{\partial y} \left(\frac{\partial f}{\partial x}\right) (which here = 0)
 
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