Derivative using Logarithmic Differentiation

In summary, the conversation is about a student seeking help with a math problem involving logarithmic differentiation. The student noticed a difference between their answer and Wolframalpha's answer and is asking for assistance in finding out where they went wrong. The reply advises the student to provide their steps using LaTeX in order for others to identify the mistake. The responder also suggests that the issue could possibly be with the use of Wolframalpha and not just the student's solution.
  • #1
marc_2094
4
0

Homework Statement



http://www.flickr.com/photos/50468243@N02/8577233960/

Homework Equations





The Attempt at a Solution



In the pic, the noticeable difference between my answer and Wolframalpha's is the tan[log(sin x+1) to base 5]. If I do logarithmic differentiation, what I get is my Answer (the one in the pic) but when I do product rule (I get the same answer with Wolframalpha). Please help. I'm confused. THanks! :)
 
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  • #2
You're not doing the logarithmic differentiation correctly.
 
  • #3
Can you please help me find out what I did wrong?
 
  • #4
marc_2094 said:
Can you please help me find out what I did wrong?

In order to do so, you will need to write out here all the steps you took to get from the problem to your answer. It would be better if you typed the steps out using LaTeX.
 
  • #5
I'll admit I didn't check your answers. It could be you're doing the product rule incorrectly. (I simply sided with Wolfram Alpha, but you may have messed up using it as well.) In any case, we can't tell where you're going wrong if all you do is post your final results. Doing so is like saying, "My car won't start. What's wrong?"
 

1. What is logarithmic differentiation?

Logarithmic differentiation is a technique used to find the derivative of a function that cannot be easily solved using traditional methods, such as the product, quotient, or chain rule. It involves taking the natural logarithm of both sides of the function and then using properties of logarithms to simplify the expression and find the derivative.

2. When should logarithmic differentiation be used?

Logarithmic differentiation should be used when the function contains products, quotients, or powers that make it difficult to find the derivative using traditional methods. It is also useful when the function contains variables in both the base and exponent of an exponential expression.

3. How do you perform logarithmic differentiation?

To perform logarithmic differentiation, follow these steps:

  1. Take the natural logarithm of both sides of the function.
  2. Use properties of logarithms to simplify the expression.
  3. Take the derivative of both sides of the function.
  4. Solve for the derivative by isolating the variable.

4. What are the benefits of using logarithmic differentiation?

Logarithmic differentiation allows us to find the derivative of functions that would otherwise be difficult to solve using traditional methods. It also allows us to avoid using the chain rule in certain cases, making the process more efficient and less prone to error.

5. Are there any limitations to using logarithmic differentiation?

Yes, there are limitations to using logarithmic differentiation. It is not always the most efficient method and may not work for all types of functions. In some cases, it may be easier to use traditional methods or numerical methods to find the derivative.

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