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