Differentiate the following with respect to x:

Given,

f(x) =

⇒ f(x) =

⇒ f(x) = a cot x + b + c cosec x

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

∴ a cot x + b + c cosec x)

Using algebra of derivatives –

⇒ f’(x) =

Use the formula:

∴ f’(x) = a( – cosec² x) + 0 + c( – cosec x cot x)

⇒ f’(x) = – a cosec² x – c cosec x cot x

∴ f’(x) = – a cosec² x – c cosec x cot x