Derivative of x + 1/2

The calculator will find the derivative of

x + \frac{1}{2}

, with steps shown.

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

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

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

The derivative of a constant is $0$ :

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

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

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

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

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

Derivative of x+12x + \frac{1}{2}x+21​