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!