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13 Differentialrechnung

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13.2 Ableitungsregeln

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13.2.2 Summenregel

$y$	$=$	$f_{1} (x) + f_{2} (x) + \dots + f_{n} (x)$
$y^{'}$	$=$	$f_{1}^{'} (x) + f_{2}^{'} (x) + \dots + f_{n}^{'} (x)$

Beispiel 13 - 1: .

	$y$	$=$	$4 x^{7} + 3 \cdot cos x - 5 e^{x} + ln x$
$\Rightarrow$	$y^{'}$	$=$	$28 x^{6} - 3 sin x - 5 e^{x} + \frac{1}{x}$

	$s (t)$	$=$	$\frac{a t^{2}}{2} + v_{0} \cdot t + S_{0}$
$\Rightarrow$	$s^{'} (t)$	$=$	$v (t)$	$=$	$a \cdot t + v_{0}$

	$v (t)$	$=$	$tanh (t) + v_{0}$
$\Rightarrow$	$v^{'} (t)$	$=$	$\frac{1}{{cosh}^{2} (t)}$	$=$	$1 - {tanh}^{2} t$