Derivada de $$$x \left(2 - 3 x\right)$$$

Aplique a regra do produto $$$\frac{d}{dx} \left(f{\left(x \right)} g{\left(x \right)}\right) = \frac{d}{dx} \left(f{\left(x \right)}\right) g{\left(x \right)} + f{\left(x \right)} \frac{d}{dx} \left(g{\left(x \right)}\right)$$$ com $$$f{\left(x \right)} = x$$$ e $$$g{\left(x \right)} = 2 - 3 x$$$:

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

A derivada de uma soma/diferença é a soma/diferença das derivadas:

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

Aplique a regra da potência $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$ com $$$n = 1$$$, em outras palavras, $$$\frac{d}{dx} \left(x\right) = 1$$$:

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

A derivada de uma constante é $$$0$$$:

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

Aplique a regra da constante multiplicativa $$$\frac{d}{dx} \left(c f{\left(x \right)}\right) = c \frac{d}{dx} \left(f{\left(x \right)}\right)$$$ com $$$c = 3$$$ e $$$f{\left(x \right)} = x$$$:

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

Aplique a regra da potência $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$ com $$$n = 1$$$, em outras palavras, $$$\frac{d}{dx} \left(x\right) = 1$$$:

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

Logo, $$$\frac{d}{dx} \left(x \left(2 - 3 x\right)\right) = 2 - 6 x$$$.