Question

Find the derivatives of the functions:$f\left(x\right)=e^{3\ln x}$

Short answer

The required answer is$3x^2$.

Step-by-step solution

Step 1. Given information. 

The given function is:$f\left(x\right)=e^{3\ln x}$

Step 2. Find the derivative of the given function.

$$\begin{gathered} f\left(x\right)=e^{3\ln x} \\ =e^{\ln x^3} \\ =x^3 \\ f\text{'}\left(x\right)=\frac{d}{dx}\left(x^3\right) \\ =3x^2 \end{gathered}$$