## How do we differentiate ln \(\left(e^{3 x}\right) ?\)

Answer:

\(\text { 3. } \frac{d}{d x}\left(\ln e^{3 x}\right)=3\)

Explanation:

I’ll answer number \(3\) for you,

Use properties of logarithms to simplify \(\ln a^{n}=n \ln a\)

\(\ln e^{3 x}=3 x \ln e\)The function \(y=\ln x\) and \(y=e^{x}\) are inverses. This means their product is \(1\).

\(=3 x\)

This, by the power rule, has derivative \(3\).

Hopefully this helps!