Question
Find the derivative \( y=\ln (2 x+3)^{4} \) Type answer \( y^{\prime}= \) (numerator)/(denominator)
Ask by Marsh Rose. in the United States
Mar 17,2025
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Answer
\( y' = \frac{8}{2x + 3} \)
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Mind Expander
To find the derivative of \( y=\ln (2x+3)^{4} \), we can start by using the properties of logarithms to simplify. First, recall that \( \ln(a^b) = b \cdot \ln(a) \). Thus, we rewrite the function as: \[ y = 4 \ln(2x + 3) \] Now, we can differentiate using the chain rule: \[ y' = 4 \cdot \frac{1}{2x + 3} \cdot (2) = \frac{8}{2x + 3} \] So, the final answer is: \[ y' = \frac{8}{2x + 3} \]