Derivative of Exponential Function with Variable Exponent

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Homework Help Overview

The discussion revolves around finding the derivative of the function y = 10^(1 - x^2), which involves the application of differentiation rules for exponential functions with variable exponents.

Discussion Character

  • Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the derivative obtained by the original poster and compare it with the output from Wolfram Alpha. There is an exploration of algebraic manipulation to verify correctness and clarity on how to express the derivative.

Discussion Status

Some participants express agreement with the original poster's derivative, while others question the interpretation of Wolfram's answer. There is a productive exchange regarding the representation of the derivative and algebraic simplifications.

Contextual Notes

Participants are navigating through potential discrepancies between their calculations and external resources, highlighting the importance of clarity in mathematical expressions and interpretations.

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Homework Statement


Find the derivative of:
y = 10^(1 - x^2)

Homework Equations


I get:
y' = (10^(1 - x^2))(ln 10)(-2x)

doing everything Wolfram does here:
http://www.wolframalpha.com/input/?i=derivative+10^(1+-+x^2)

I don't understand why it simplifies to Wolfram's final answer from what I got.

The Attempt at a Solution


Everything Wolfram does above.
 
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Your answer is fine. Wolfram's answer is weird.
 
But it's a great opportunity to use algebra to see if you're correct!

-22-x251-x2xln10

-21+1-x251-x2xln10

-2121-x251-x2xln10

-2(21-x251-x2)xln10

-2xln10(101-x2)
 
vela said:
Your answer is fine. Wolfram's answer is weird.

Thank you. BTW I wouldn't multiply the (10^(1 - x^2)) by (-2x) to get something like -20x^(1 - x^2) right? I'd write (-2x)(10^(1 - x^2))(ln 10)?
 
Right.
 
As in the latter?
 
Yes.
 
Alright then. Thanks a bunch : D
 

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