Q:

Definition derivative of function f

$$\text{Compute by definition derivative of function f in point } x_0,\text{ where}$$
$$ f(x)=\frac{4}{1+x^2}-\tan x, \quad x_0=\frac{\pi}{4} $$
I would be very grace for help with solving this example, because I don't know what's going on with this "counting  by definition".

A:

Consider a differential quotient $$\frac{f(x)-f\left(\dfrac{\pi}{4}\right)}{x-\dfrac{\pi}{4}}$$ and find its limit as $x\to\dfrac{\pi}{4}$. That's it.

