Differentiate the following functions with respect to x:

(1 – 2 tan x)(5 + 4 sin x)

Let, y = (1 – 2 tan x)(5 + 4 sin 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 = (1 – 2tan x) and v = (5 + 4sin 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 = (1 – 2tan x)

∴

⇒

⇒ …..equation 2 {∵ }

As, v = 5 + 4sin x

⇒

⇒ …equation 3 {∵ }

∴ from equation 1, we can find dy/dx

∴

using equation 2 & 3, we get –

⇒

⇒

∵ sin x = tan x cos x , so we get –

⇒

Hence,