Find the derivative of function cosec x x. - Vidyadip

Question

Find the derivative of function $cosec\ x \cot x.$

✓

Answer

Here $f (x) = cosec\ x \cot x$
$\therefore f'(x) = \frac{d}{{dx}} [cosec\ x \cot x]$
$= cosec\ x \frac{d}{{dx}}\ (\cot x) + \cot x \frac{d}{{dx}} (cosec\ x)$
$= cosec\ x . – cosec^2 x + \cot x . – cosec\ x \cot x$
$= - cosec^3 x – cosec\ x \cot^2 x.$

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