compute (x-1)(x+2)(x-3) then differentiate the result

Let's calculate:

(x - 1) \cdot (x + 2) \cdot (x - 3)

(x \cdot x

+ x \cdot 2

- 1 \cdot x

- 1 \cdot 2) \cdot (x - 3)

(x^{2}

+ x \cdot 2

- x

- 2) \cdot (x - 3)

(x^{2} + x - 2) \cdot (x - 3)

x^{2} x

+ x^{2} \cdot -3

+ x \cdot x

+ x \cdot -3

- 2 x

- 2 \cdot -3

x^{3}

- x^{2} \cdot 3

+ x^{2}

- x \cdot 3

- 2 x

+ 6

x^{3}

- 2 x^{2}

- 5 x

+ 6

Let's differentiate:

{(x^{3} - 2 x^{2} - 5 x + 6)}^{'}

{(x^{3})}^{'}

+ {(- 2 x^{2})}^{'}

+ {(- 5 x)}^{'}

+ 0

3 x^{2} - 2 \cdot 2 x - 5

▷Result: $3 x^{2} - 4 x - 5$