Find the derivative $$ y=\ln (2 x+3)^{4} $$ Type answer $$ y^{\prime}= $$ (numerator)/(denominator)

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We start with the function
$$
y = \ln \left((2x+3)^4\right).
$$

Using the logarithm property, we can rewrite the function as
$$
y = 4 \ln(2x+3).
$$

Taking the derivative with respect to $$ x $$:

1. Differentiate the constant multiplier:
   $$
   y' = 4 \cdot \frac{d}{dx} \left(\ln(2x+3)\right).
   $$
   
2. Use the chain rule for the derivative of the logarithm:
   $$
   \frac{d}{dx} \left(\ln(2x+3)\right) = \frac{1}{2x+3} \cdot \frac{d}{dx}(2x+3).
   $$
   Since
   $$
   \frac{d}{dx}(2x+3) = 2,
   $$
   this becomes:
   $$
   \frac{d}{dx} \left(\ln(2x+3)\right) = \frac{2}{2x+3}.
   $$
   
3. Multiply by the constant:
   $$
   y' = 4 \cdot \frac{2}{2x+3} = \frac{8}{2x+3}.
   $$

Thus, the derivative is 
$$
y'=\frac{8}{2x+3}.
$$
$$ y' = \frac{8}{2x + 3} $$

Find the derivative \( y=\ln (2 x+3)^{4} \) Type answer \( y^{\prime}= \) (numerator)/(denominator)

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