y = ln [sin (2 x - 3)]

1. Substitution:

u = (2 x - 3)

2. Substitution:

v = sin (u)

$y^{'}$	$=$	$\frac{d y}{d v} \cdot \frac{d v}{d x}$	$=$	$\frac{d y}{d v} \cdot \frac{d v}{d u} \cdot \frac{d u}{d x}$

$\frac{d u}{d x}$	$=$	$\frac{d (2 x - 3)}{d x}$	$=$	$2$
$\frac{d v}{d u}$	$=$	$\frac{d (sin (u))}{d u}$	$=$	$cos (u)$
$\frac{d y}{d v}$	$=$	$\frac{d (ln (v))}{d v}$	$=$	$\frac{1}{v}$

$y^{'}$	$=$	$\frac{1}{v} \cdot cos (u) \cdot 2$	$=$	$\frac{1}{sin (u)} \cdot cos (u) \cdot 2$
	$=$	$2 \cdot cot (u)$	$=$	$2 cot (2 x - 3)$

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Weiteres Beispiel:

{(\frac{1}{l n (x)})}^{'} = (\frac{- \frac{1}{x}}{{(l n (x))}^{2}})