Question

Find the second order derivative of the function.

tan^–1 x

Answer 1

Let, y = tan^–1 x

Differentiating both sides with respect to x,

`dy/dx = d/dx tan^-1 x`

= `1/((1 + x^2))`

Differentiating both sides again with respect to x,

`(d^2 y)/dx^2 = d/dx 1/((1 + x^2))`

= `((1 + x^2) d/dx (1) - (1) d/dx (1 + x^2))/(1 + x^2)^2`

= `((1 + x^2) xx 0 - 1 xx (0 + 2x))/(1 + x^2)^2`

= `(0 - 2x)/(1 + x^2)^2`

= `(-2x)/(1 + x^2)^2`