Find the derivative of ln(6x2 - 1) with respect to x.

Question

ScanSolve AI Tutor · Accepted Answer

To solve this, we will find the derivative of the given expression $\ln(6x^2 - 1)$ with respect to $x$ . We will use the chain rule.

Identify the outer and inner functions.
Let $y = \ln(u)$ , where $u = 6x^2 - 1$ .
Differentiate the outer function with respect to $u$ .
The derivative of $\ln(u)$ is $\frac{1}{u}$ .
$\frac{d}{du}(\ln(u)) = \frac{1}{u}$
Differentiate the inner function with respect to $x$ .
The derivative of $6x^2 - 1$ is $12x$ .
$\frac{du}{dx} = \frac{d}{dx}(6x^2 - 1) = 12x$
Apply the chain rule.
The chain rule states that $\frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx}$ .
Substitute the results from Step 2 and Step 3:
$\frac{dy}{dx} = \frac{1}{6x^2 - 1} \cdot 12x$ $\frac{dy}{dx} = \frac{12x}{6x^2 - 1}$
The derivative of $\ln(6x^2 - 1)$ is:
$\frac{12x}{6x^2 - 1}$

Answer