Find the derivative of `tan (2x+ 5)` with respect to x by using first principle of derivative.

Explanation

`f'(x)lim_(h->0)(f(x+h)-f(x))/(x+h-x)`

`f'(x)=lim_(h->0)(tan(2(x+h)+5)-tan(2x+5))/h`

`lim_(h->0)(sin(2x+2h+5))/(cos(2x+2h+5))`

`lim_(h->0)(sin(2x+2h+5-2x-5))/(cos(2x+2h+5)*cos(2x+5)h)`

`lim_(h->0)(sin2h)/(2h)1/(cos(2x+2h+5)cos(2x+5)`

`2/(cos(2x+5)*cos(2x+5))`

`2/(cos^2(2x+5)`

`2sec^2(2x+5)`.