Question

Find the second order derivatives of the function x^2+3x+2

Answer 1

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I LOVE DERIVATIVE QUESTIONS...

FIRST DERIVATIVE.......
let y= x^2+3x+2
now diffrentiate on both sides.
dy/dx= d/dx(x^2+3x+2)
dy/dx=2x+3.....eqn.1
hence this is first derivative


SECOND ORDER DERIVATIVE....
now from 1 equation .
differentiate eq1 again.

d^2y/dx^2=2
hence this is second derivative


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Answer 2

Let function , y = x² + 3x + 2
now differentiate y with respect to x
$\frac{dy}{dx}=\frac{d(x^2)}{dx}+\frac{d(3x)}{dx}+\frac{d(2)}{dx}\\=2x^{2-1}+3x^{1-1}+0\\\\\frac{dy}{dx}=2x+3$
hence, 1st order derivatives of the function is $\frac{dy}{dx}=2x+3$
for finding 2nd order derivatives , differentiate $\frac{dy}{dx}$ once again,
e.g., $\frac{d}{dx}(dy/dx)=\frac{d(2x+3)}{dx}\\\\\frac{d^2y}{dx^2}=2x^{1-1}=2$

hence, $\frac{d^2y}{dx^2}=2$