Question

Use the chain rule to prove that$\frac{d}{dx}\left(e^{kx}\right)=k{e}^{kx}$

Short answer

The given function has been proved.

Step-by-step solution

Step 1. Given Information

The given derivative is$\frac{d}{dx}\left(e^{kx}\right)$

Step 2. Proof

As we know that $\frac{d}{dx}\left(e^x\right)=e^x$. So, we get,

$$\begin{gathered} \frac{d}{dx}\left(e^{kx}\right)=e^{kx}\frac{d}{dx}\left(kx\right) \\ =k{e}^{kx} \end{gathered}$$

Hence, Proved!