Learn the Derivative Rule for Logarithmic Functions | Step-by-Step Explanation

  • Thread starter Tom McCurdy
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In summary, the conversation discussed the topic of derivatives and how to calculate them. The speaker provided a step-by-step explanation and also mentioned the use of the chain rule. They also shared a helpful website for further assistance.
  • #1
Tom McCurdy
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My friend asked for some help with derviatives, I said I would explain here then link him

Here is how you do it

[tex] \frac {d}{dx} log_b(x) = \frac {1}{xlnb} [/tex]
 
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  • #2
so you have at first
[tex] \frac {d}{dx} log_{10}(10/x) = \frac {1}{\frac{10}{x}ln10} [/tex]

which simplifies to

[tex] \frac {x}{10ln(10} [/tex]

now you may think your done, but you need to remember the chain rule so you have

[tex] \frac {x}{10ln(10} + \frac {d}{dx} \frac {10}{x}[/tex]

so let's take the quotient rule and solve for [tex] \frac {10}{x}[/tex]

f(x) = 10 f'(x)=0
g(x) = x g'(x)=1

g(x)f'(x)-f(x)g'(x)
----------------
g(x)^2

x*0-10*1
---------
x^2

=
[tex] \frac {-10}{x^2} [/tex]

so then muliply

[tex] \frac {x}{10ln(10)} * \frac {-10}{x^2} [/tex]

and you will get

[tex]\frac {d}{dx} log_{10}(10/x)= \frac {-1}{ln(10)*x} [/tex]
 
  • #3
Any other help you could probably use this website address
http://people.hofstra.edu/faculty/Stefan_Waner/RealWorld/tutorials/unit3_3.html [Broken]
 
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1. What is the derivative rule for logarithmic functions?

The derivative rule for logarithmic functions states that the derivative of a logarithmic function is equal to the reciprocal of the function's argument multiplied by the derivative of the argument.

2. Why is it important to learn the derivative rule for logarithmic functions?

Understanding the derivative rule for logarithmic functions is crucial for solving problems involving logarithmic functions, as well as for more advanced calculus and physics concepts.

3. How do you apply the derivative rule for logarithmic functions?

To apply the derivative rule for logarithmic functions, you first take the natural logarithm of the function and then use the power rule to find the derivative. You can then substitute the original function back in for the argument in the derivative.

4. Are there any special cases or exceptions to the derivative rule for logarithmic functions?

Yes, there are a few special cases to consider when using the derivative rule for logarithmic functions. These include logarithmic functions with a base other than e, as well as functions with multiple logarithmic terms or logarithms within other functions.

5. How can I practice and improve my understanding of the derivative rule for logarithmic functions?

The best way to practice and improve your understanding of the derivative rule for logarithmic functions is to work through various practice problems and examples. You can also seek out additional resources and explanations, or consult with a tutor or classmate for assistance.

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