Finding the Derivative of Trigonometric Functions with Exponents?

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Homework Help Overview

The discussion revolves around finding the derivative of the function 5^(sin(theta)), which involves trigonometric functions and exponentiation. Participants are exploring methods to differentiate this expression with respect to the variable theta.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • The original poster expresses uncertainty about how to approach the differentiation, suggesting a lack of clarity on the relevant variable and method. Some participants suggest using logarithmic differentiation, while others mention the chain rule as an alternative approach.

Discussion Status

The discussion is active, with participants sharing different methods for differentiation. Guidance has been offered regarding the use of logarithmic differentiation and the chain rule, indicating a productive exchange of ideas. However, there is no explicit consensus on a single method being preferred.

Contextual Notes

The original poster has indicated difficulty in finding resources or guidance on this specific problem, which may suggest a gap in understanding or available information on the topic.

Taryn
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hey I have this question and have looked it up in the textbook and web sites but can't seem to find what to do!
Any assistance would be appreciated thanks!

Find the first derivative w.r.t the relevant variable
5^(sin(theta))

I am guessin the relevant variable is theta but I don't even no where to go from that!
 
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First thing is to write it as

y = 5^sin(theta)

Then take logs of both sides and differentiate implicitly to get dy/dtheta. :smile:
 
haha, that's helpful! I don't know y I didnt think of that, thanks so much! Appreciate it!
 
Or, if you're feeling less industrious, the chain rule also works.
 
But to use the chain rule, you have to know that the derivative of 5x is (ln(5))5x.
 

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