Question

derivatives of logarithmic functions: problem 1 (1 point) let ( f(x)=ln(e^{x}) ) ( f(x)=square ) ( f(e^{4})=square ) note: you can earn partial credit on this problem. preview my answers submit answers you have attempted this problem 0 times. you have unlimited attempts remaining.

Explanation:

Step1: Simplify the function

First, use the property of logarithms $\ln(a^b)=b\ln(a)$. So, $f(x)=\ln(e^{4}) = 4\ln(e)$. Since $\ln(e) = 1$, then $f(x)=4$.

Step2: Find the derivative

The derivative of a constant function $y = C$ (where $C$ is a constant) is $y'=0$. So, $f'(x)=0$.

Step3: Evaluate at a point

Since $f'(x) = 0$ for all $x$, then $f'(e^{4})=0$.

Answer:

$f'(x)=0$, $f'(e^{4})=0$