Im trying to find the partial derivative of df/dy, but im not sure how to differentiate tan^-1 (x/y).
could someone check if i differentiated the log correctly?
Thanks!
That's correct but a very strange way of writing the answer!
I would, instead, have used the fact that the derivative of is . Let so that . Also and .
By the chain rule, then, .
But, as I said, AllenCuz's result is also correct- These answers are exactly the same.
Imagine a right triangle with angle , "opposite side" of length x, and "near side" of length y. Then so [tex]/theta= tan^{-1}(\frac{x}{y}). But then the hypotenuse of the triangle has length and so that .
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