what is the derivative of arctan

The derivative of arctan x is 1/(1+x^2) . To derive the derivative of arctan, assume that y = arctan x, then tan y = x. Differentiating both sides with respect to y, then sec^2 y = dx/dy. Taking reciprocal on both sides, dy/dx = 1/(sec^2 y) = 1/(1+tan^2 y) = 1/(1+x^2) . Another way to derive the derivative of arctan x is to use the formula for the derivative of an inverse function. Let y = arctan x, then x = tan y. Differentiating both sides with respect to x, we get 1 = sec^2 y dy/dx. Solving for dy/dx, we get dy/dx = 1/(sec^2 y) = 1/(1+tan^2 y) = 1/(1+x^2) .