View Full Version : Need hint on 'simple' differentiation problem
redshift
Dec1-04, 04:07 AM
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 (http://www-math.mit.edu/~djk/18_01/chapter20/proof02.html).
dextercioby
Dec1-04, 04:57 AM
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
Dec1-04, 07:08 AM
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
Dec1-04, 07:41 AM
z'= \frac{1}{1+(\frac{y}{x})^2} \(-\frac{y}{x^2}\)
by the chain rule.
Now multiply both numerator and denominator by x2.
Apparently the sofware didn't read the paranthesis you've written,so it should be:
z'= \frac{1}{1+(\frac{y}{x})^2} (-\frac{y}{x^2}) =-\frac{y}{x^2+y^2}
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