Here,

y = sin (x^x) ……(i)

Let ……(ii)

Taking log on both sides,

log u = log

log u = x log x

Differentiating both sides with respect to x,

[from (ii)]

Now, using equation (ii) in (i)

y = sin u

Differentiating both sides with respect to x,

Using equation (ii) and (iii),

Hence Proved.