Find the derivative $$ y=\ln (3 x+1) $$ Type answer $$ y^{\prime}= $$ (numerator)/(denominator) $$ \square $$

Question

UpStudy AI · Accepted Answer

1. Given $$ y = \ln(3x+1) $$.

2. Differentiate using the chain rule:
   $$
   y' = \frac{d}{dx} \ln(u) \cdot \frac{du}{dx} \quad \text{where} \quad u = 3x+1.
   $$

3. The derivative of $$ \ln(u) $$ is $$\frac{1}{u}$$ and the derivative of $$ u = 3x+1 $$ is $$ 3 $$:
   $$
   y' = \frac{1}{3x+1} \cdot 3.
   $$

4. Simplify the expression:
   $$
   y' = \frac{3}{3x+1}.
   $$

$$ y^{\prime}=\frac{3}{3x+1} $$
$$ y^{\prime}=\frac{3}{3x+1} $$

Find the derivative
Type answer (numerator)/(denominator)