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Derivative of $$$2 x_{0}$$$
Related calculators: Logarithmic Differentiation Calculator, Implicit Differentiation Calculator with Steps
Your Input
Find $$$\frac{d}{dx_{0}} \left(2 x_{0}\right)$$$.
Solution
Apply the constant multiple rule $$$\frac{d}{dx_{0}} \left(c f{\left(x_{0} \right)}\right) = c \frac{d}{dx_{0}} \left(f{\left(x_{0} \right)}\right)$$$ with $$$c = 2$$$ and $$$f{\left(x_{0} \right)} = x_{0}$$$:
$${\color{red}\left(\frac{d}{dx_{0}} \left(2 x_{0}\right)\right)} = {\color{red}\left(2 \frac{d}{dx_{0}} \left(x_{0}\right)\right)}$$Apply the power rule $$$\frac{d}{dx_{0}} \left(x_{0}^{n}\right) = n x_{0}^{n - 1}$$$ with $$$n = 1$$$, in other words, $$$\frac{d}{dx_{0}} \left(x_{0}\right) = 1$$$:
$$2 {\color{red}\left(\frac{d}{dx_{0}} \left(x_{0}\right)\right)} = 2 {\color{red}\left(1\right)}$$Thus, $$$\frac{d}{dx_{0}} \left(2 x_{0}\right) = 2$$$.
Answer
$$$\frac{d}{dx_{0}} \left(2 x_{0}\right) = 2$$$A