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Derivative of $$$3 x + 2$$$
Related calculators: Logarithmic Differentiation Calculator, Implicit Differentiation Calculator with Steps
Your Input
Find $$$\frac{d}{dx} \left(3 x + 2\right)$$$.
Solution
The derivative of a sum/difference is the sum/difference of derivatives:
$${\color{red}\left(\frac{d}{dx} \left(3 x + 2\right)\right)} = {\color{red}\left(\frac{d}{dx} \left(3 x\right) + \frac{d}{dx} \left(2\right)\right)}$$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 $$$c = 3$$$ and $$$f{\left(x \right)} = x$$$:
$${\color{red}\left(\frac{d}{dx} \left(3 x\right)\right)} + \frac{d}{dx} \left(2\right) = {\color{red}\left(3 \frac{d}{dx} \left(x\right)\right)} + \frac{d}{dx} \left(2\right)$$Apply the power rule $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$ with $$$n = 1$$$, in other words, $$$\frac{d}{dx} \left(x\right) = 1$$$:
$$3 {\color{red}\left(\frac{d}{dx} \left(x\right)\right)} + \frac{d}{dx} \left(2\right) = 3 {\color{red}\left(1\right)} + \frac{d}{dx} \left(2\right)$$The derivative of a constant is $$$0$$$:
$${\color{red}\left(\frac{d}{dx} \left(2\right)\right)} + 3 = {\color{red}\left(0\right)} + 3$$Thus, $$$\frac{d}{dx} \left(3 x + 2\right) = 3$$$.
Answer
$$$\frac{d}{dx} \left(3 x + 2\right) = 3$$$A