Question

What is the derivative of $e^{2x}$?

Answer 1

Derivative formula:

$\frac{d}{dx}\left(e^x\right)=e^x$

Chain rule: $\frac{d}{dx}\left(f\left(g\left(x\right)\right)\right)=f\text{'}\left(g\left(x\right)\right)·g\text{'}\left(x\right)$

The derivative of $e^{2x}$ is,

Differentiate $e^{2x}$ with respect to $x$, using the chain rule

$\frac{d}{dx}\left(e^{2x}\right)=\frac{d\left(e^{2x}\right)}{d\left(2x\right)}.\frac{d\left(2x\right)}{dx}[U\sin gchainrule]$

$\Rightarrow$ $\frac{d}{dx}{e}^{2x}=e^{2x}·2$

$\Rightarrow$ $\frac{d}{dx}{e}^{2x}=2e^{2x}$

Hence, the derivative of $e^{2x}$ is $2e^{2x}$.