Question

Find the derivatives of the functions:$f\left(x\right)=x^{-3}{e}^{2x}$

Short answer

The required answer is$2x^{-3}{e}^{2x}-3x^{-4}{e}^{2x}$.

Step-by-step solution

Step 1. Given information. 

The given function is:$f\left(x\right)=x^{-3}{e}^{2x}$

Step 2. Find the derivative of the given function.

$$\begin{gathered} f\left(x\right)=x^{-3}{e}^{2x} \\ f\text{'}\left(x\right)=\frac{d}{dx}\left(x^{-3}{e}^{2x}\right) \\ =x^{-3}\frac{d}{dx}{e}^{2x}+e^{2x}\frac{d}{dx}{x}^{-3} \\ =2x^{-3}{e}^{2x}-3x^{-4}{e}^{2x} \end{gathered}$$