Question

sinx
26
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Find the derivative of (x2-3x+2)(x+2)wrt x.
Find the mean deviation about of first fi​

Answer 1

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;

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

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;

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

Answer 2

Solution:

$\pink{(x^2-3x+2)(x+2)=x(x^2-3x+2)+2(x^2-3x+2)}$

$\pink{x^3-3x^2+2x^2-6x+4}$

$\pink{x^3-x^2-4x+4}$

Lets differentiating x

Therefore d/dx${(x^3-x^2-4x+4)}$

Lets substitute it

${3×x^3-1 \ - 2×x^2-1 \ - 1×4×x^1-1}$

Therefore $\pink{3x^2-2x-4}$