Differentiate the following functions with respect to x:

Let, y =

We have to find dy/dx

As we can observe that y is a fraction of two functions say u and v where,

u = sin x – x cos x and v = x sin x + cos x

∴ y = u/v

As we know that to find the derivative of fraction of two function we apply quotient rule of differentiation.

By quotient rule, we have –

…equation 1

u = – (x cos x – sin x)

Using algebra of derivatives –

⇒

∵

∴ {using product rule}

⇒ …equation 2

As, v = x sin x + cos x

∴

Using algebra of derivatives –

⇒

∵

∴ {using product rule}

⇒ …equation 3

∴ from equation 1, we can find dy/dx

∴

using equation 2 and 3, we get –

⇒

⇒

⇒

Hence,