Answer:
A
Step-by-step explanation:
We are given the function:
[tex]\displaystyle f(x) = e^x[/tex]
And we want to determine the value of:
[tex]\displaystyle \ln (f'(2))[/tex]
First, find f'. We can take the derivative of both sides with respect to x:
[tex]\displaystyle \begin{aligned} f'(x) & = \frac{d}{dx}\left[ e^x\right] \\ \\ &= e^x \end{aligned}[/tex]
Find f'(2):
[tex]\displaystyle \begin{aligned}f'(2) & = e^{(2)} \\ \\ & = e^2 \end{aligned}[/tex]
We can take the natural logarith of both sides:
[tex]\displaystyle \ln (f'(2)) = \ln e^2[/tex]
Simplify. In conclusion:
[tex]\displaystyle \ln (f'(2)) = 2[/tex]
Our answer is A.
