Explanation:

To solve this question, we must know what potential ENERGY is???

Potential energy is the energy possessed by an object by the virtue of its position

In simple words, Potential energy is the STORED energy of an object due to its position

Now, Potential energy can be divided into two:-

i) Gravitational Potential Energy

ii) Elastic Potential Energy

The formula that we are deriving here is BASED on Gravitational Potential Energy

Gravitational potential energy is the energy stored in an object as the RESULT of its vertical position or height. The energy is stored as the result of the gravitational attraction of the Earth for the object.

Now, we know that

Work done is the same as energy

then, Potential energy must ALSO be equal to work done ---- 1

We know,

Work done = Force × Displacement

W = F × s

and F = ma

Now, since we are talking about Gravitational Potential Energy, Force applied is due to acceleration due to gravity

So, F = Mass × Acceleration due to gravity

F = m × g ---- 2

Now, s is the didplacement, in case of Gravitational Potential Energy,

Displacement is nothing but Height ----- 3

Thus,

W = F × s

From eq.1 we get,

P.E = F × s

From eq.2 and eq.3 we get,

P.E. = m × g × h

Thus,

P.E. = mgh

Hope it helped and you understood it........All the best