# If y=xsin x<

Let u = xsin x

Taking log both sides,

log u = sin x log x

On differentiating,

Let, v = sin (xx)

Let, t = xx

log t = x log x

On differentiating,

Using (2),

As, y = u + v

So,

From (1) and (3),

OR

y = log (1 + 2t2 + t4)

Applying the formula (a + b)2 = a2 + b2 + 2ab in (1 + 2t2 + t4).

y = log (1+t2)2

As log xn = n log x

y = 2 log (1+t2)

On differentiating,

x = tan-1 t

On differentiating,

Now,

Again differentiating,

=4(1+t2)

Therefore,

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