Differentiate the following functions with respect to x:

x³ e^x cos x

Let, y = x³ e^x cos 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 = x³

v = cos x

w = e^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 = x³

∴ …equation 2 {∵ }

As, v = cos x

…equation 3 {∵ }

As, w = e^x

∴ …equation 4 {∵ }

∴ from equation 1, we can find dy/dx

∴

using equation 2, 3 & 4, we have –

⇒

Hence,