If then write the value of f’(x).  [CBSE 2014]

Given

Let us first integrate and find f(x)

Using uv rule where u and v are functions of x

Here u = t and v = sint

⇒ f(x) = - xcosx + sinx

f’(x) means differentiating function with respect to x

Using uv rule for differentiation where u and v are functions of x

⇒ (uv)’ = u’v + uv’

⇒ f’(x) = - (1cosx + x(-sinx)) + cosx

⇒ f’(x) = - cosx + xsinx + cosx

⇒ f’(x) = xsinx