Sinx2627Find the derivative of (x2-3x+2)(x+2)wrt x.Find the mean devia

1.	Sinx2627Find the derivative of (x2-3x+2)(x+2)wrt x.Find the mean deviation about of first fi
Answer» Question:- Find the DERIVATIVE of (x² - 3x + 2)(x + 2) wrt x. Answer:- METHOD - 1:- $\implies \sf \: \dfrac{d}{dx} (x ^2 - 3x + 2)(x + 2)$ USING; d/dx (uv) = v × du/dx + u × dv/dx we get; $\implies \sf \: (x + 2) \times \frac{d}{dx} ( {x}^{2} - 3x + 2) + (x ^{2} - 3x + 2) \times \frac{d}{dx} (x + 2) \\ \\ \\ \implies \sf \:(x + 2) \times (2 \times {x}^{2 - 1} - 3 \times {x}^{1 - 1} + 0) + ( {x}^{2} - 3x + 2)(1 \times {x}^{1 - 1} + 0) \\ \\ ( \because \sf \frac{d}{dx} (constant) = 0 \: \: \& \: \: \frac{d}{dx} ( {x})^{n} = n \times {x}^{n - 1} \: ) \\ \\ \\ \implies \sf \: (x + 2)(2x - 3) + ( {x}^{2} - 3x + 2)(1) \\ \\ \\ \implies \sf \: x(2x - 3) + 2(2x - 3) + {x}^{2} - 3x + 2 \\ \\ \\ \implies \sf \: 2 {x}^{2} - 3x + <klux>4X</klux> - 6 + {x}^{2} - 3x + 2 \\ \\ \\ \implies \boxed{\sf \: 3 {x}^{2} - 2x - 4}$ Method - 2:- (x² - 3x + 2)(x + 2) = x(x² - 3x + 2) + 2(x² - 3x + 2) = x³ - 3x² + 2x + 2x² - 6x + 4 = x³ - x² - 4x + 4 Now, DIFFERENTIATING with respect to x we get; $\implies \sf \: \frac{d}{dx} ( {x}^{3} - {x}^{2} - 4x +4 ) \\ \\ \\ \implies \sf \:3 \times {x}^{3 - 1} - 2 \times {x}^{2 - 1} - 1 \times 4 \times \times {x}^{1 - 1} + 0 \\ \\ \\ \\ \implies \boxed{ \sf \: 3 {x}^{2} - 2x - 4}$

Sinx2627Find the derivative of (x2-3x+2)(x+2)wrt x.Find the mean deviation about of first fi

Answer»

Question:-

Find the DERIVATIVE of (x² - 3x + 2)(x + 2) wrt x.

Answer:-

METHOD - 1:-

$\implies \sf \: \dfrac{d}{dx} (x ^2 - 3x + 2)(x + 2)$

USING;

d/dx (uv) = v × du/dx + u × dv/dx we get;

$\implies \sf \: (x + 2) \times \frac{d}{dx} ( {x}^{2} - 3x + 2) + (x ^{2} - 3x + 2) \times \frac{d}{dx} (x + 2) \\ \\ \\ \implies \sf \:(x + 2) \times (2 \times {x}^{2 - 1} - 3 \times {x}^{1 - 1} + 0) + ( {x}^{2} - 3x + 2)(1 \times {x}^{1 - 1} + 0) \\ \\ ( \because \sf \frac{d}{dx} (constant) = 0 \: \: \& \: \: \frac{d}{dx} ( {x})^{n} = n \times {x}^{n - 1} \: ) \\ \\ \\ \implies \sf \: (x + 2)(2x - 3) + ( {x}^{2} - 3x + 2)(1) \\ \\ \\ \implies \sf \: x(2x - 3) + 2(2x - 3) + {x}^{2} - 3x + 2 \\ \\ \\ \implies \sf \: 2 {x}^{2} - 3x + <klux>4X</klux> - 6 + {x}^{2} - 3x + 2 \\ \\ \\ \implies \boxed{\sf \: 3 {x}^{2} - 2x - 4}$

Method - 2:-

(x² - 3x + 2)(x + 2) = x(x² - 3x + 2) + 2(x² - 3x + 2)

= x³ - 3x² + 2x + 2x² - 6x + 4

= x³ - x² - 4x + 4

Now,

DIFFERENTIATING with respect to x we get;

$\implies \sf \: \frac{d}{dx} ( {x}^{3} - {x}^{2} - 4x +4 ) \\ \\ \\ \implies \sf \:3 \times {x}^{3 - 1} - 2 \times {x}^{2 - 1} - 1 \times 4 \times \times {x}^{1 - 1} + 0 \\ \\ \\ \\ \implies \boxed{ \sf \: 3 {x}^{2} - 2x - 4}$