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