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Derivative of $$$\frac{\sqrt{2} x}{2 \left|{\sigma}\right|}$$$ with respect to $$$x$$$
Related calculators: Logarithmic Differentiation Calculator, Implicit Differentiation Calculator with Steps
Your Input
Find $$$\frac{d}{dx} \left(\frac{\sqrt{2} x}{2 \left|{\sigma}\right|}\right)$$$.
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 $$$c = \frac{\sqrt{2}}{2 \left|{\sigma}\right|}$$$ and $$$f{\left(x \right)} = x$$$:
$${\color{red}\left(\frac{d}{dx} \left(\frac{\sqrt{2} x}{2 \left|{\sigma}\right|}\right)\right)} = {\color{red}\left(\frac{\sqrt{2}}{2 \left|{\sigma}\right|} \frac{d}{dx} \left(x\right)\right)}$$Apply the power rule $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$ with $$$n = 1$$$, in other words, $$$\frac{d}{dx} \left(x\right) = 1$$$:
$$\frac{\sqrt{2} {\color{red}\left(\frac{d}{dx} \left(x\right)\right)}}{2 \left|{\sigma}\right|} = \frac{\sqrt{2} {\color{red}\left(1\right)}}{2 \left|{\sigma}\right|}$$Thus, $$$\frac{d}{dx} \left(\frac{\sqrt{2} x}{2 \left|{\sigma}\right|}\right) = \frac{\sqrt{2}}{2 \left|{\sigma}\right|}$$$.
Answer
$$$\frac{d}{dx} \left(\frac{\sqrt{2} x}{2 \left|{\sigma}\right|}\right) = \frac{\sqrt{2}}{2 \left|{\sigma}\right|}$$$A