Question

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

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:

Step-by-step explanation:

Here we are finding second order derivative of function y with respect to x.

So,we have to differentiate the function two times.

d/dx (x^n)= nx^(n-1)d/dx(constant)=0

We calculate dy/dx first and then d/dx(dy/dx) and get the answer.

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