Differentiate the functions given in w.r.t. x.

Given:

Let y=

Let y = u + v

Taking log on both sides, we get

⇒log u = x.log(x cos x)

⇒ log u = x(log x + log (cos x))

⇒ log u = x(log x) +x(log (cos x))

Now, differentiate both sides with respect to x

Taking log on both sides, we get

Now, differentiate both sides with respect to x

Because, y = u + v