Question

I have a 12th grade AP calculus question picture including about derivatives

Answer 1

The given functions are

`\begin{gathered} f(x)=e^x \\ \\ g(x)=ln(x) \end{gathered}`

Since we need to find the derivative of g(x)

Then we will use

`x(dy)/(dx)=1`

Divide both sides by x

`(dy)/(dx)=(1)/(x)`

Plug in (lnx) for y

`(d)/(dx)ln(x)=(1)/(x)`

Then

`[ln(x)]^(\prime)=(1)/(x)`

From here we can say

`g^(\prime)(x)=(1)/(x)`