Derivative of $$$5 w$$$
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Your Input
Find $$$\frac{d}{dw} \left(5 w\right)$$$.
Solution
Apply the constant multiple rule $$$\frac{d}{dw} \left(c f{\left(w \right)}\right) = c \frac{d}{dw} \left(f{\left(w \right)}\right)$$$ with $$$c = 5$$$ and $$$f{\left(w \right)} = w$$$:
$${\color{red}\left(\frac{d}{dw} \left(5 w\right)\right)} = {\color{red}\left(5 \frac{d}{dw} \left(w\right)\right)}$$Apply the power rule $$$\frac{d}{dw} \left(w^{n}\right) = n w^{n - 1}$$$ with $$$n = 1$$$, in other words, $$$\frac{d}{dw} \left(w\right) = 1$$$:
$$5 {\color{red}\left(\frac{d}{dw} \left(w\right)\right)} = 5 {\color{red}\left(1\right)}$$Thus, $$$\frac{d}{dw} \left(5 w\right) = 5$$$.
Answer
$$$\frac{d}{dw} \left(5 w\right) = 5$$$A