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Derivative of $$$n x$$$ with respect to $$$x$$$
Related calculators: Logarithmic Differentiation Calculator, Implicit Differentiation Calculator with Steps
Your Input
Find $$$\frac{d}{dx} \left(n x\right)$$$.
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 $$$c = n$$$ and $$$f{\left(x \right)} = x$$$:
$${\color{red}\left(\frac{d}{dx} \left(n x\right)\right)} = {\color{red}\left(n \frac{d}{dx} \left(x\right)\right)}$$Apply the power rule $$$\frac{d}{dx} \left(x^{m}\right) = m x^{m - 1}$$$ with $$$m = 1$$$, in other words, $$$\frac{d}{dx} \left(x\right) = 1$$$:
$$n {\color{red}\left(\frac{d}{dx} \left(x\right)\right)} = n {\color{red}\left(1\right)}$$Thus, $$$\frac{d}{dx} \left(n x\right) = n$$$.
Answer
$$$\frac{d}{dx} \left(n x\right) = n$$$A
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