Calculating the Derivative of the Inverse Function Using the Chain Rule

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    Derivative Inverse
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Discussion Overview

The discussion revolves around calculating the derivative of the inverse function using the chain rule, specifically for the function F(X) = e^-(x^2) + 3x. Participants are examining the derivative at a specific point, x = 1, and identifying mistakes in the initial calculation.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant presents a calculation for the derivative of the inverse function and claims to find D/DX (F^-1(x)) at x = 1.
  • Another participant asserts that the derivative of F is incorrect without specifying the nature of the error.
  • A third participant questions the correctness of the derivative provided, suggesting that the calculation may be flawed.
  • It is pointed out that the derivative of a sum should include all terms, indicating that the derivative of the second term (3x) was omitted in the initial calculation.
  • A participant explicitly states that the "+3" part of the function was missed in the derivative calculation.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correctness of the initial derivative calculation, as there are multiple claims of error and differing perspectives on what constitutes the mistake.

Contextual Notes

There are unresolved aspects regarding the correct application of the chain rule and the handling of derivatives of sums, which may affect the conclusions drawn from the discussion.

huan.conchito
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F(X) = e^-(x^2)+3x. Find D/DX (F^-1(x)) a x = 1.
Here's what i did, where is my mistake?
F(0)=1 therefore F^-1(1)=0
F'(x)= - 2xe^-(x^2)
d/dx (f^-1(x)) = 1/ F'(f^-1(x)) = 1/[-2(1)e^(-(1)^2)] = 1/2e^-1 = e / 2
 
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The derivative of F is incorrect.
 
-2x* e^(-X^2)
how is it incorrect?
 
The derivative of a sum is the sum of the derivatives. You haven't added the derivative of the second term in your function, F(x) = e-x2 + 3x.
 
You missed the "+3" part of it.

Daniel.
 
thank you very much
 

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