# Need hint on 'simple' differentiation problem

I need to differentiate z = artan(y/x) with respect to x. Somehow z' = y/(1 +(1/x)^2) doesn't seem right.

The derivative of arctan x = 1/(1 + x^2). There's a proof of that here.

dextercioby
Homework Helper
redshift said:
I need to differentiate z = artan(y/x) with respect to x. Somehow z' = y/(1 +(1/x)^2) doesn't seem right.

You know that
$$[\arctan(f(x))]'=\frac{f'(x)}{1+f^2 (x)}$$
,so apply the formula correctly.This is of course if "y" and "x" are independent variables.

HallsofIvy
Homework Helper
$$z'= \frac{1}{1+(\frac{y}{x})^2} $$-\frac{y}{x^2}$$$$
by the chain rule.

Now multiply both numerator and denominator by x2.

dextercioby
$$z'= \frac{1}{1+(\frac{y}{x})^2} $$-\frac{y}{x^2}$$$$
$$z'= \frac{1}{1+(\frac{y}{x})^2} (-\frac{y}{x^2}) =-\frac{y}{x^2+y^2}$$