Question

Second derivative for tan^-1x

Answer 1

Answer:

questions

is improper check the error and display question properly

Answer 2

Answer:

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

Step-by-step explanation:

let y=tan^-1x

tany=x. --------------------------(1)

differentiation of respect with x :-

sec^2y dy/dx=1

now using trigonometry formula:-

(1+tan^2y)dy/dx=1

(1+x^2)dy/dx=1 [by eq.1]

dy/dx=1/(1+x^2)

now

again differentiate

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

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

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