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Derivative of $$$4 e^{x}$$$
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Your Input
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, $$$\frac{d}{dx} \left(4 e^{x}\right) = 4 e^{x}$$$.
Answer
$$$\frac{d}{dx} \left(4 e^{x}\right) = 4 e^{x}$$$A