# Need help on finding derivatives of logarithmic functions

• jzq
Use the chain rule when necessary (in the logarithm).In summary, the conversation discusses the derivatives of ln(x) and provides examples of how to use the product rule and chain rule to find the derivative of functions involving ln(x).
jzq
These are the problems (Please, just point me in the right direction):

$$y=x^{2}\ln(6x)$$

$$f(x)=x\ln(12x)$$

Do you know the derivative of ln(x)?

whozum said:
Do you know the derivative of ln(x)?
1/x

10 char

The product rule -- d(uv)/dx = u'v + uv'
[edit: sorry had the answers, didnt know he didnt want to know them]

Last edited:
$$y = x^2ln(6x)$$

$$\frac{dy}{dx} = \frac{d(x^2ln(6x))}{dx}$$

which is of the form

$$\frac{d(u(x)v(x))}{dx} = u\frac{dv}{dx} + v\frac{du}{dx}$$

Use the chain rule when necessary (in the logarithm).

## 1. What is the general formula for finding the derivative of a logarithmic function?

The general formula for finding the derivative of a logarithmic function is:
d/dx (log base a (x)) = 1 / (x * ln(a))

## 2. How do I find the derivative of a logarithmic function with a different base?

To find the derivative of a logarithmic function with a different base, you can use the formula:
d/dx (log base a (x)) = 1 / (x * ln(a))
and then substitute the base of your logarithmic function for "a" in the formula.

## 3. Can I use the chain rule to find the derivative of a logarithmic function?

Yes, you can use the chain rule to find the derivative of a logarithmic function. You will need to apply the chain rule to the entire function, including both the log and the argument inside the log.

## 4. How do I find the derivative of a composite logarithmic function?

To find the derivative of a composite logarithmic function, you will need to use the chain rule and the general formula for finding the derivative of a logarithmic function.
For example, if you have a function: f(x) = log base a (x^2),
you can find the derivative by using the formula:
d/dx (log base a (x)) = 1 / (x * ln(a))
and then applying the chain rule to the argument inside the log (in this case, x^2).

## 5. Are there any special properties or rules for finding the derivative of a logarithmic function?

Yes, there are a few special properties and rules for finding the derivative of a logarithmic function. Some of these include:
- The derivative of ln(x) is 1/x
- The derivative of log base a (x) is 1 / (x * ln(a))
- The derivative of log base a (f(x)) is 1 / (f(x) * ln(a)) * f'(x)
- The logarithmic functions follow the same rules for finding derivatives as other functions, such as the power rule and product rule.

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