Q 25. - Calculus

Question

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

Step-by-Step Solution

Answer

The required answer is $3x^2$.

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.

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