Using Log Theorem to Derive Terms in Calculus 2

In summary, The conversation is about a student who missed learning about the "log theorem" in their Calculus 1 class and is now being told by their teacher that it is necessary to use this theorem in order for their terms to be corrected on exams. The student has not been able to find an explanation or theorem for the "log theorem" online. They are also struggling to understand how their teacher got a certain answer using the "log theorem" and are asking for clarification. Other students in the conversation suggest that the "log theorem" could possibly refer to logarithmic differentiation or the sum of logarithms.
  • #1
Chocolaty
48
0
I'm taking cal 2 right now and i missed the part in cal 1 where he talked about "log theorem". Now this guy tells us that he's lazy when he corrects exams and if we don't use the log theorem to derive a term then he won't correct that term. I've looked on the net but couldn't find explanation or theorem.

Here's an example of a term where he used it.
cos[(3x-2)^4]

When i derive this term I use the generalized power rule:
[u(x)]^n => n*u^(n-1)*u'
cos[(3x-2)^4] => -sin[(3x-2)^4]*4(3x-2)^3*(3)
He came up with this answer:
-2(3x-2)^4*4(3x-2)^3*(3)

Can anybody explain to me how one uses the log theorem?
 
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  • #2
I have never heard of that before, and I definitely don't see how it's possible to get what you're teacher got for that derivative. Your way seems correct, so maybe you should ask you're teacher what the "log theorem" is..
 
  • #3
ok.

Does anybody know what this term actually means?
ln( x y )
There's no plus or minus or whatever.
 
  • #4
Chocolaty said:
ok.

Does anybody know what this term actually means?
ln( x y )
There's no plus or minus or whatever.


Is it maybe supposed to mean, ln( f(x,y) ) where f(x,y) is a function of the two variables x and y?
 
  • #5
Maybe he means logarithmic differentiation. That wouldn't work for the function you gave though.
 
  • #6
Chocolaty said:
ok.

Does anybody know what this term actually means?
ln( x y )
There's no plus or minus or whatever.
looks like log x+ log y to me!
 

1. What is the Log Theorem in Calculus 2?

The Log Theorem, also known as the Logarithmic Differentiation Theorem, is a rule in calculus that allows us to find derivatives of functions that are not easily differentiable using the standard rules. It states that the derivative of a function can be found by taking the logarithm of the function and then differentiating it using the standard rules.

2. How do you use the Log Theorem to derive terms in Calculus 2?

To use the Log Theorem, you first take the logarithm of the function you want to differentiate. Then, you can use the properties of logarithms to simplify the expression. Finally, you can differentiate the expression using the standard rules of differentiation. This will give you the derivative of the original function.

3. Why is the Log Theorem useful in Calculus 2?

The Log Theorem is useful because it allows us to find derivatives of functions that are not easily differentiable using the standard rules. This is especially helpful in Calculus 2, where we often encounter more complex functions that cannot be differentiated using the basic rules.

4. What are some common mistakes when using the Log Theorem in Calculus 2?

One common mistake when using the Log Theorem is forgetting to take the logarithm of the function before differentiating it. Another mistake is not simplifying the expression using the properties of logarithms before differentiating. It is also important to pay attention to the domain of the function and make sure it is valid for taking the logarithm.

5. Can the Log Theorem be used for all functions in Calculus 2?

No, the Log Theorem can only be used for functions that can be written in the form of a power, such as y = x^a. It cannot be used for trigonometric, exponential, or logarithmic functions.

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