Solving the Derivative of 4^xlog_9(x) Without Logs

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In summary, the derivative of 4^xlog<sub>9</sub>(x) can be simplified by factoring out 4^xlog<sub>9</sub>(x) and the purpose of solving it without using logarithms is to practice using the product rule and chain rule in calculus. There are no shortcuts or tricks to solving this derivative and the same method can be applied to solve the derivative of other functions.
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Weave
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Homework Statement


Ok, so our professor gives us homework online which we submit online, its called webwork. This one equation I found the derivitive of. Heres the thing, the program will not evalute answers with log base other than 10.

Homework Equations


The equation is:
[tex]y=4^xlog_{9}(x)[/tex]
This is the derivitive
[tex]4^xln(4)log_{9}(x)+\frac{4^x}{xln(9)}[/tex]

The Attempt at a Solution


How do I express this by having no logs?
 
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  • #2
Never mind,,
i realized I have to use the change of base formula, lol
 

FAQ: Solving the Derivative of 4^xlog_9(x) Without Logs

What is the derivative of 4^xlog9(x) without using logarithms?

The derivative of 4^xlog9(x) is 4^xlog9(x)ln(4) + 4^xlog9(x)/xln(9). This can be derived using the product rule and the chain rule.

Can the derivative of 4^xlog9(x) be simplified?

Yes, the derivative can be simplified by factoring out 4^xlog9(x) from both terms in the derivative. This results in 4^xlog9(x)(ln(4) + 1/xln(9)).

What is the purpose of solving the derivative of 4^xlog9(x) without using logarithms?

The purpose of solving the derivative without using logarithms is to practice using the product rule and chain rule in calculus. It also allows for a deeper understanding of derivatives and their applications.

Are there any shortcuts or tricks to solving this derivative?

No, there are no shortcuts or tricks to solving this derivative without using logarithms. It requires a thorough understanding of the product rule and chain rule in calculus.

Can the same method be used to solve the derivative of other functions?

Yes, the same method of using the product rule and chain rule can be applied to solve the derivative of other functions. However, the specific steps may vary depending on the function.

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