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I'm just beginning to study Diff Geom, in an introductory chapter I've stumbled upon a problem of expressing laplace equation in polar coordinates. I've found the solution of this problem and at one point in the solution second partial derivative of V by X is calculated. I do not understand why the way they calculate it is correct.

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P.S. I understand how the 1st member is calculated, but not the other members.

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    The book doesn't do this derivation? What an odd book. In this case, I think including the image is fine, btw. Thanks for acknowledging that we prefer it to be typed, though. :) – 2017-01-07
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    The original book doesn't have a solution. The solution is from lecture notes I've found. – 2017-01-07
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    Well, this isn't really my area, but I'd be amazed if this wasn't in most books on the subject. – 2017-01-07
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    @Moo If you simply multiply the expressions in parenthesis, you will not get the final result. I've tried it and it didn't work. – 2017-01-07
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    It's one differential operator acting on another: you have by the product rule $ \partial_t (f(t) \partial_t) = f'(t) \partial_t + f(t) \partial_t^2 $. – 2017-01-07
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    @Chappers It looks you are right. I'll check it out. Thanks. – 2017-01-07

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