Turunan dari $$$x^{2} - 3 x + 6$$$

Turunan dari jumlah/selisih adalah jumlah/selisih dari turunan:

$${\color{red}\left(\frac{d}{dx} \left(x^{2} - 3 x + 6\right)\right)} = {\color{red}\left(\frac{d}{dx} \left(x^{2}\right) - \frac{d}{dx} \left(3 x\right) + \frac{d}{dx} \left(6\right)\right)}$$

Terapkan aturan pangkat $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$ dengan $$$n = 2$$$:

$${\color{red}\left(\frac{d}{dx} \left(x^{2}\right)\right)} + \frac{d}{dx} \left(6\right) - \frac{d}{dx} \left(3 x\right) = {\color{red}\left(2 x\right)} + \frac{d}{dx} \left(6\right) - \frac{d}{dx} \left(3 x\right)$$

Terapkan aturan kelipatan konstanta $$$\frac{d}{dx} \left(c f{\left(x \right)}\right) = c \frac{d}{dx} \left(f{\left(x \right)}\right)$$$ dengan $$$c = 3$$$ dan $$$f{\left(x \right)} = x$$$:

$$2 x - {\color{red}\left(\frac{d}{dx} \left(3 x\right)\right)} + \frac{d}{dx} \left(6\right) = 2 x - {\color{red}\left(3 \frac{d}{dx} \left(x\right)\right)} + \frac{d}{dx} \left(6\right)$$

Terapkan aturan pangkat $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$ dengan $$$n = 1$$$, dengan kata lain, $$$\frac{d}{dx} \left(x\right) = 1$$$:

$$2 x - 3 {\color{red}\left(\frac{d}{dx} \left(x\right)\right)} + \frac{d}{dx} \left(6\right) = 2 x - 3 {\color{red}\left(1\right)} + \frac{d}{dx} \left(6\right)$$

Turunan dari suatu konstanta adalah $$$0$$$:

$$2 x + {\color{red}\left(\frac{d}{dx} \left(6\right)\right)} - 3 = 2 x + {\color{red}\left(0\right)} - 3$$

Dengan demikian, $$$\frac{d}{dx} \left(x^{2} - 3 x + 6\right) = 2 x - 3$$$.