Derivative of 2*x + 1

The calculator will find the derivative of

2 x + 1

, with steps shown.

Your Input

Find $\frac{d}{dx} \left(2 x + 1\right)$ .

Solution

The derivative of a sum/difference is the sum/difference of derivatives:

{\color{red}\left(\frac{d}{dx} \left(2 x + 1\right)\right)} = {\color{red}\left(\frac{d}{dx} \left(2 x\right) + \frac{d}{dx} \left(1\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 $c = 2$ and $f{\left(x \right)} = x$ :

{\color{red}\left(\frac{d}{dx} \left(2 x\right)\right)} + \frac{d}{dx} \left(1\right) = {\color{red}\left(2 \frac{d}{dx} \left(x\right)\right)} + \frac{d}{dx} \left(1\right)

Apply the power rule $\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$ with $n = 1$ , in other words, $\frac{d}{dx} \left(x\right) = 1$ :

2 {\color{red}\left(\frac{d}{dx} \left(x\right)\right)} + \frac{d}{dx} \left(1\right) = 2 {\color{red}\left(1\right)} + \frac{d}{dx} \left(1\right)

The derivative of a constant is $0$ :

{\color{red}\left(\frac{d}{dx} \left(1\right)\right)} + 2 = {\color{red}\left(0\right)} + 2

Thus, $\frac{d}{dx} \left(2 x + 1\right) = 2$ .

Answer

$\frac{d}{dx} \left(2 x + 1\right) = 2$ A

Derivative of 2x+12 x + 12x+1

Your Input

Solution

Answer

Derivative of $2 x + 1$