Exponential Derivative problem

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Homework Help Overview

The discussion revolves around the differentiation of an exponential function, specifically the derivative of the function dy/dθ = 2·3^(−θ). Participants are exploring the process of finding the derivative and clarifying steps involved in the calculation.

Discussion Character

  • Mathematical reasoning, Problem interpretation, Assumption checking

Approaches and Questions Raised

  • Participants discuss the differentiation process, with one original poster attempting to apply the chain rule. Questions arise regarding the clarity of the steps taken and the assumptions made about the differentiation of the exponent.

Discussion Status

Some participants are seeking clarification on the differentiation steps, while others have identified potential mistakes in the original poster's reasoning. There is an acknowledgment of a mistake related to differentiating the exponent, but no consensus on the final answer has been reached.

Contextual Notes

One participant notes that they initially forgot to differentiate the exponent, which may have contributed to confusion. There is also a suggestion regarding the placement of ln(3) in the expression, indicating a possible misunderstanding of the derivative's structure.

Painguy
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Homework Statement


dy/dθ =2·3^(−θ)


Homework Equations


The Attempt at a Solution


2*(d/dθ)(3^(-θ)
2(3^(-θ)ln(3))
(2ln(3))/(3^θ)

I keep getting this wrong and I'm not sure why. Could someone point out my mistake?
 
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Could you maybe make your step-by-step process a little clearer? It's a little difficult for me to follow you.

Also, I assume we're solving for y given y'?
 
I already got it. Sorry for bothering you guys. My problem was that I forgot to differentiate -theta in 3^(-theta).

The final answer I have is -2*3^(-θ)ln(3)
 
That ln(3) should be in the denominator I think.
 

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