What is escape velocity? What is the derivation for escape velocity?

Definition:
The velocity required for an object to escape from the gravitational influence of the planet is known as escape velocity.
escape velocity for an object is 11.2km/s.

Expression for escape velocity:

Consider a body of mass 'm' projected vertically upwards from the surface of the earth with velocity ve. In other to escape from the gravitational pull of the earth ,the body should be given kinetic energy which is equal to the potential energy of the body.

Gravitational potential energy = -GMm / R

Kinetic energy =1/2 mve2

----> 1/2 mve2 = GMm / R

----> 1/2 ve2 = GM / R

----> Ve2 = 2GM / R

But g = GM / R2

----> GM = gR2

Substituting the value;

----> ve2 = 2/R (gR2) = 2gR

----> ve2 = √2gR.