Projectile Motion - derivation of horizontal range

The derivation of the horizontal range and maximum height of a projectile launched with a given velocity at a given angle.

[@ibrahimzyiadh7826]

thank you

[@ummeyhabiba3793]

can you please tell me that why do we use derivative of something with respect to something to find the maximum quantity of that particular thing?

[@ferntheyoutuber9960]

First!