Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):
cosec x cot x

Question

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): cosec x cot x

Philoid · Accepted Answer

Let f(x) = cosec x cot x

By product rule

f’(x) = cosec x (cot x)’ + cot x (cosec x)’ ……..(1)

Let f₁(x) = cot x, accordingly f₁(x + h) = cot (x + h)

By first principle

=

∴ (cot x)’ = - cosec² x ………………..(2)

Let f₂(x) = cosec x, accordingly f₂(x + h) = cosec (x + h)

By first principle

=

= -cosec x cot x

∴ (cosec x)’ = -cosec x cot x ……………….(3)

Putting the value of (2) and (3) in (1)

f’(x) = cosec x (-cosec² x) + cot x (-cosec x cot x)

= - cosec³ x – cot² x cosec x

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):cosec x cot x

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):
cosec x cot x