Find the derivative.
-$f(x)=e^{x} \log _{8}|x|$
A) $e^{x} \log _{8}|x|+\frac{e^{x}}{x \ln 8}$
B) $e^{x}+\frac{1}{x \ln 8}$
C) $e^{x} \log _{8}|x|+\frac{e^{x}}{8 x}$
D) e $e^{x} \log _{8}|x|+\frac{e^{x} \log _{8}|x|}{x}$

Question

Quizplus · Accepted Answer

The derivative of $f(x)=e^{x} \log _{8}|x|$ is found using the product rule and the chain rule. The derivative of $e^x$ is $e^x$, and the derivative of $\log_{8}|x|$ is $\frac{1}{x \ln 8}$. Applying the product rule gives $e^{x} \log _{8}|x| + e^{x} \cdot \frac{1}{x \ln 8}$.

Find the Derivative f(x)=exlog⁡8∣x∣f(x)=e^{x} \log _{8}|x|f(x)=exlog8​∣x∣ A) exlog⁡8∣x∣+exxln⁡8e^{x} \log _{8}|x|+\frac{e^{x}}{x \ln 8}exlog8​∣x∣+xln8ex​

Find the Derivative $f(x)=e^{x} \log _{8}|x|$ A) $e^{x} \log _{8}|x|+\frac{e^{x}}{x \ln 8}$