Question

given the function $f(x)=e^{2x}$, determine the derivative of $f$ at $x = 5$ using the limit shown below. you do not have to simplify your answer. answer attempt 1 out of 2 $lim_{x
ightarrow5}$

Explanation:

Step1: Recall derivative limit - definition

The derivative of a function $y = f(x)$ at $x = a$ is given by $f^{\prime}(a)=\lim_{x
ightarrow a}\frac{f(x)-f(a)}{x - a}$. Here, $a = 5$ and $f(x)=e^{2x}$, $f(5)=e^{2\times5}=e^{10}$. So, $f^{\prime}(5)=\lim_{x
ightarrow5}\frac{e^{2x}-e^{10}}{x - 5}$.

Answer:

$\lim_{x
ightarrow5}\frac{e^{2x}-e^{10}}{x - 5}$