First Order Partial Derivatives of a Function

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SUMMARY

The discussion focuses on finding the first order partial derivatives of the function \( f(x,y) = \ln\left|\frac{x+\sqrt{x^2+y^2}}{x-\sqrt{x^2+y^2}}\right| \) at the point (4,3). Participants explore various simplification techniques, including the application of logarithmic rules and differentiation methods. Key insights include the importance of correctly applying the chain rule and recognizing the limitations of logarithmic identities. Ultimately, the conversation emphasizes the need for careful algebraic manipulation to derive the correct expressions for the partial derivatives.

PREREQUISITES
  • Understanding of first order partial derivatives
  • Familiarity with logarithmic differentiation
  • Knowledge of the chain rule in calculus
  • Basic algebraic manipulation skills
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  • Study the application of the chain rule in multivariable calculus
  • Learn about logarithmic differentiation techniques
  • Explore the properties of logarithms and their applications in calculus
  • Practice finding partial derivatives of complex functions
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Students and professionals in mathematics, engineering, and physics who are working with multivariable calculus and need to understand partial derivatives and their applications.

  • #31
ok once again thanks Voko you have been brilliant!

f(x)= [1+(x^2+y^2)^{-1/2}(x)] [\frac{1}{x+\sqrt{x^2+y^2}} - \frac{1}{x-\sqrt{x^2+y^2}}]

So this is written correctly then?
 
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  • #32
Again, the second term is incorrect. You cannot go from (-a)(b) to -(-ab), but that's what you insist on doing. (-a)(b) = -(ab).
 

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