Question

d^2y/dx
^2 if y =x^3-6x^2+7x+6
Find

Answer 1

Rules :

    • d/dx (xⁿ) = n xⁿ⁻¹

    • d/dx (any constant) = 0

Solution :

Given y = x³ - 6x² + 7x + 6

Differentiating both sides with respect to x, we get

dy/dx = d/dx (x³ - 6x² + 7x + 6)

= d/dx (x³) - 6 d/dx (x²) + 7 d/dx (x) + d/dx (6)

= 3x² - 12x + 7

or, dy/dx = 3x² - 12x + 7

Again Differentiating both sides with respect to x, we get

d²y/dx² = d/dx (3x² - 12x + 7)

= d/dx (3x²) - 12 d/dx (x) + d/dx (7)

= 6x - 12

or, d²y/dx² = 6x - 12

Answer 2

Answer:

$\frac{dy}{dx} = \frac{d}{dx} ( {x}^{3} - 6 {x}^{2} + 7x + 6) \\ = \frac{d}{dx} ( {x}^{3} ) - 6 \frac{d}{dx} ( {x}^{2} ) + 7 \frac{d}{dx} (x) + \frac{d}{dx} (6)= 3 {x}^{2} - 12x + 7 \\ \frac{ {d}^{2} }{d {x}^{2} } = \frac{d}{dx} (3 {x}^{2} - 12x + 7) \\ = \frac{d}{dx} (3 {x}^{2} ) - 12 \frac{d}{dx} (x) + \frac{d}{dx} (7) \\ = 6x - 12$