Mean value theorem with trigonometric functions Let $f(x) = 2\arctan(x) + \arcsin\left(\frac{2x}{1+x^2}\right)$


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*Show that $f(x)$ is defined for every $ x\ge 1$

*Calculate $f'(x)$ within this range

*Conclude that $f(x) = \pi$ for every $ x\ge 1$
Can I get some hints how to start? I don't know how to start proving that  $f(x)$ is defined for every $ x\ge 1$ and I even had problems calculating $f'(x)$
Thanks everyone!

Hint
Recall that the $\arctan$ function is defined on $\Bbb R$ while the $\arcsin$ function is defined on $[-1,1]$. Compute the derivative $f'(x)$ and prove that it's equal to $0$. Conclude that $f$ is a constant which we can determinate by taking the limit of $f$ at $+\infty$ 
