Question

What is the derivative of `arctan(cosθ)`?

Answer 1

`-sintheta/(1 +cos^2theta)`

Explanation:

using the following facts :

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

differentiating using the`color(blue)(" chain rule ")`

`d/dx[f(g(x))] = f'g(x).g'(x)`

`d/dx[tan^-1(costheta)] = 1/(1 + cos^2theta) d/dx(costheta)`

`= -sintheta/(1+ cos^2theta)`