# Thread: Logarithmic function

1. ## Logarithmic function

Deriving 4x^3 + ln y^2 + 2y = 2x

I think the first step is; 12x^2 + 1 / y^2 + and here is where I'm stuck. What is the derivative of the 2y and 2x?

2. Originally Posted by Archduke01
Deriving 4x^3 + ln y^2 + 2y = 2x

I think the first step is; 12x^2 + 1 / y^2 + and here is where I'm stuck. What is the derivative of the 2y and 2x?
You have to use implicit differentiation. This should be easy, I think it is the $ln(y^2)$ term that is confusing you.

One of the properties of logarithms allows you to write:

$ln(y^2)=2ln(y)$

Use the chain rule to differentiation this:

$2\frac{d}{dx}ln(y)=\frac{2}{y}\frac{dy}{dx}$

That should help.

3. Originally Posted by adkinsjr
You have to use implicit differentiation. This should be easy, I think it is the $ln(y^2)$ term that is confusing you.

One of the properties of logarithms allows you to write:

$ln(y^2)=2ln(y)$

Use the chain rule to differentiation this:

$2\frac{d}{dx}ln(y)=\frac{2}{y}\frac{dy}{dx}$

That should help.
What does the 2y and the 2x become?

4. Originally Posted by Archduke01
What does the 2y and the 2x become?
Does the 2y become 2yy'? What does the 2x become?