Question

Differentiate the function

Answer 1

\[f(x) = \log_{5} (xe^x)\]

Answer 2

As a start : convert it to natural log by using change of base formula

Answer 3

So would it look like \[5 \ln (xe^x)\] @ganeshie8 ?

Answer 4

\[\rm f(x) = \log_{5} (xe^x) = \frac{\log_{e} (xe^x)}{\log_e( 5)} = \frac{\ln (xe^x)}{\ln( 5)}\]

Answer 5

ln(5) is just a number so you can factor it out and take the derivative of remaining function using chain rule

Answer 6

\[\rm {\begin{align}\left[f(x)\right]' &= \frac{1}{\ln (5)}\left[\ln (xe^x)\right]'\\~\\
&= \frac{1}{\ln (5)} \cdot \frac{1}{xe^x}\cdot \left[xe^x\right]'\\~\\

\end{align} }\]

Answer 7

use product rule to differentiate that piece