Given :

To Prove :

Formulae :

i)

ii)

iii)

iv)

v)

vi)

Answer :

Given equation,

Let

Therefore, y = s + t ………eq(1)

I. For

let

therefore,

Differentiating above equation w.r.t. x,

…………. By chain rule

………….

………

………eq(2)

II. For

let

therefore,

Differentiating above equation w.r.t. x,

…………. By chain rule

………….

………

………eq(2)

Differentiating eq(1) w.r.t. x,

………

= -1 -1 ………from eq(2) and eq(3)

= -2

Hence proved !!!