The differential for P = 0.2x² -17x -10 is P' = 0.4x - 17Step-by-step explanation:Let us revise how to differentiate an equation with respect to xIf the equation is [tex]y = ax^{n}+b[/tex] , where a , b are constantThe differentiation of the term [tex]ax^{n}[/tex] is [tex]a(n)x^{(n-1)}[/tex] (multiply the coefficient of x by the power"n" and subtract 1 from the power)The differentiation of the term b is 0, because b is a constantThe differentiation of y is [tex]\frac{dy}{dx}=a(n)x^{(n-1)}+0=a(n)x^{(n-1)}[/tex]You can write [tex]\frac{dy}{dx}[/tex] as y'∵ P = 0.2x² - 17x - 10- Let us differentiate each term∵ The differentiation of 0.2x² is [tex]0.2(2)x^{2-1}=0.4x^{1}=0.4x[/tex]∵ The differentiation of -17x is [tex]-17(1)x^{1-1}=-17x^{0}=-17(1)=-17[/tex]∵ The differentiation of -10 is zero because the differentiation of the numerical term is 0∴ The differentiation of P is P' = 0.4x - 17The differential for P = 0.2x² -17x -10 is P' = 0.4x - 17Learn more:You can learn more about the differentiation in brainly.com/question/4279146#LearnwithBrainly