Differentiate the following with respect to x:

2 sec x + 3 cot x – 4 tan x

Given,

f(x) = 2 sec x + 3 cot x – 4 tan x

we need to find f’(x), so differentiating both sides with respect to x –

∴ 2 sec x + 3 cot x – 4 tan x)

Using algebra of derivatives –

⇒ f’(x) =

Use the formula:

∴ f’(x) = 2(sec x tan x) + 3( – cosec² x) – 4(sec² x)

⇒ f’(x) = 2sec x tan x – 3cosec² x – 4sec² x

∴ f’(x) = 2sec x tan x – 3cosec² x – 4sec² x