Need hint on 'simple' differentiation problem

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

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  • #2
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The derivative of arctan x = 1/(1 + x^2). There's a proof of that here.
 
  • #3
dextercioby
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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
[tex] [\arctan(f(x))]'=\frac{f'(x)}{1+f^2 (x)} [/tex]
,so apply the formula correctly.This is of course if "y" and "x" are independent variables.
 
  • #4
HallsofIvy
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[tex] z'= \frac{1}{1+(\frac{y}{x})^2} \(-\frac{y}{x^2}\)[/tex]
by the chain rule.

Now multiply both numerator and denominator by x2.
 
  • #5
dextercioby
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HallsofIvy said:
[tex] z'= \frac{1}{1+(\frac{y}{x})^2} \(-\frac{y}{x^2}\)[/tex]
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:
[tex]z'= \frac{1}{1+(\frac{y}{x})^2} (-\frac{y}{x^2}) =-\frac{y}{x^2+y^2}[/tex]
 

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