Here,

y

y = U + V + W

……(1)

Where, u ,v ,w

u

Taking log on both sides,

log u = log

log u

log u

Again, Taking log on both sides,

log log u = log

loglog u

Differentiating both sides with respect to x by using the product rule,

Put value of u and log u,

……(A)

Now,

v

taking log on both sides,

log v = log

log v

Differentiating both sides with respect to x by using the product rule,

Put value of v,

……(B)

Now ,

w =

taking log on both sides,

log w = log

log w

log w

taking log both sides,

log log w

Differentiating both sides with respect to x by using the product rule,

Put the value of w and log w,

Using equation A, B and C in equation (1),

Hence, proved.