=tan^-1(x)

Question

Use first principle to differentiate.

Answer 1

I'm assuming that you want to differentiate y = tan^(-1)(x).

Then x = tan(y)

dx/dy = sec^2(y)

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

dx/dy = 1 + x^2

dy/dx = 1/(1 + x^2)