​ Find d^2y/dx^2 of the following 1. y = x^2 + 3x + 2 ​2. y = tan^-1x

Question

Find \(\frac{d^2y}{dx^2}\) of the following

1. y = x² + 3x + 2 

2. y = tan^-1x 

Answer 1

1. Given; 

y = x² + 3x + 2

Dierentiating with respect to x;

\(\frac{dy}{dx}\) = 2x + 3

Dierentiating again with respect to x;

\(\frac{d^2y}{dx^2}\) = 2

2. Given; 

y = tan^-1x
Differentiating with respect to x; \(\frac{dy}{dx} = \frac{1}{1+x^2}\)

Differentiating again with respect to x;

\(\frac{d^2y}{dx^2}\) = -\(\frac{1}{(1+x^2)^2}.2x\).