Differentiate the following functions with respect to x:

x² sin x log x

Let, y = x² sin x log x

We have to find dy/dx

As we can observe that y is a product of three functions say u, v & w where,

u = x²

v = sin x

w = log x

∴ y = uvw

As we know that to find the derivative of product of three function we apply product rule of differentiation.

By product rule, we have –

…equation 1

As, u = x²

∴ …equation 2 {∵ }

As, v = sin x

…equation 3 {∵ }

As, w = log x

∴ …equation 4 {∵ }

∴ from equation 1, we can find dy/dx

∴

using equation 2, 3 & 4, we have –

⇒

Hence,