Question

If $f\left(x\right)=\tan x$, find $f^{\prime }\left(x\right)$ and hence find $f^{\prime }\left(\frac{\pi }{4}\right)$.

Answer 1

$f\left(x\right)=\tan x$

$f^{\prime }\left(x\right)={\sec }^{2}x$

$f^{\prime }\left(\frac{\pi }{4}\right)={\sec }^2\left(\frac{\pi }{4}\right)={\left(\sqrt{2}\right)}^2=2$