TITLE: Classical Mechanics, The Theoretical Minimum: error in answer to partial derivatives exercise?
QUESTION [0 upvotes]: I'm reading Leonard Susskind's Classical Mechanics, The Theoretical Minimum, and I'm on the interlude on partial derivatives. There is an exercise that asks you to find all of the first and second order partial derivatives of the following function,
$V(x,y) = (x/y) e^{x^2+y^2}$
I've successfully found the first derivative w.r.t. x,
$\frac{\partial}{\partial x} V(x,y) =  \frac{e^{x^2+y^2}}{y}(1+2x^2)$
But my answer for the second derivative doesn't match the answers given here,
$\frac{\partial^2}{\partial^2 x} V(x,y) = \frac{e^{x^2+y^2}}{y}(2x)(2x^2 + 3)$
A quick wolfram alpha search seems to agree with my answer, is this correct?

REPLY [0 votes]: Your answer is correct.
Solution in the pdf is correct until last step (also in the middle when he splits partial derivative of $(2x^2+1) e^a /y$ but magically corrects in next step) .
In the last step he applies chain rule incorrectly.
Chain rule applied while calculating first derivative is also incorrect but answer is correct (idk how).
Overall not a good book/source to start learning. (I feel).
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