Partial Differentiation

Haven't done this in ages, is my answer and working correct?

Q) Find both

\frac{\partial f}{\partial x}

and

\frac{\partial^2 f}{\partial x \partial y}

when

f(x,y) = ln(x^2 + y^2)

.

So I got the first part ok to be

\frac{2x}{x^2 + y^2}

The I used the chain rule and did some working and got this which I am unsure is correct

\frac{0 (x^2 + y^2) - (2x)(2y)}{(x^2 + y^2)^2}

The final answer I got was

\frac{-4xy}{(x^2 + y^2)^2}

. I'm just unsure about my working above.

Original post by 3 Phase Duck

...

All correct.

Original post by Lord of the Flies

All correct.

Cheers

Trying to remember this stuff is so frustrating when you don't have notes.

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