Need hint on 'simple' differentiation problem

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    Differentiation
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Homework Help Overview

The discussion revolves around differentiating the function z = arctan(y/x) with respect to x, focusing on the application of differentiation rules and the chain rule in calculus.

Discussion Character

  • Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants explore the differentiation of the arctangent function, questioning the correctness of initial derivative expressions and discussing the application of the chain rule.

Discussion Status

Some participants provide insights into the differentiation process and suggest applying known derivative formulas. There is an ongoing examination of the expressions used, with multiple interpretations of the derivative being discussed.

Contextual Notes

There is a mention of the independence of variables y and x, which may influence the differentiation approach. Participants also note potential issues with notation and clarity in the expressions presented.

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