# Derivative of $4 e^{x}$

The calculator will find the derivative of $4 e^{x}$, with steps shown.

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Find $\frac{d}{dx} \left(4 e^{x}\right)$.

### Solution

Apply the constant multiple rule $\frac{d}{dx} \left(c f{\left(x \right)}\right) = c \frac{d}{dx} \left(f{\left(x \right)}\right)$ with $c = 4$ and $f{\left(x \right)} = e^{x}$:

$${\color{red}\left(\frac{d}{dx} \left(4 e^{x}\right)\right)} = {\color{red}\left(4 \frac{d}{dx} \left(e^{x}\right)\right)}$$

The derivative of the exponential is $\frac{d}{dx} \left(e^{x}\right) = e^{x}$:

$$4 {\color{red}\left(\frac{d}{dx} \left(e^{x}\right)\right)} = 4 {\color{red}\left(e^{x}\right)}$$

Thus, $\frac{d}{dx} \left(4 e^{x}\right) = 4 e^{x}$.

$\frac{d}{dx} \left(4 e^{x}\right) = 4 e^{x}$A