$h(x) = \frac{1}{f(x)}$

cosec x = \frac{1}{s i n x} cosec^{2} x = \frac{1}{s i n ^{2} x} sec x = \frac{1}{c o s x} cot x = \frac{1}{t a n x}

Rules for differentiating $\frac{1}{f(x)}$

$f(x)$	$f'(x)$
$\tan kx$	$k\sec^{2}kx$
$\sec kx$	$k \sec kx \times \tan kx$
$\cot kx$	$-k \space \text{cosec}^2 \space kx$
$\text{cosec } kx$	$-k \space \text{cosec} \space kx \times \cot kx$

arcsin x = sin^{- 1} x arccos x = cos^{- 1} x arctan x = tan^{- 1} x