Differentiate the following functions with respect to x:

x⁴ (5 sin x – 3 cos x)

Let, y = x⁴ (5sin x – 3cos x)

We have to find dy/dx

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

u = x⁴ and v = 5sin x – 3cos x

∴ y = uv

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

By product rule, we have –

…equation 1

As, u = x⁴

∴ …equation 2 {∵ }

As, v = 5sin x – 3cos x

Using:

⇒ …equation 3

∴ from equation 1, we can find dy/dx

∴

⇒ {using equation 2 & 3}

Hence,