derivative of 1000(1+x/(12)^{60})

Lösung

\frac{d}{d x} (1000 (1 + \frac{x}{12})^{60})

5000 (\frac{x}{12} + 1)^{59}

Schritte zur Lösung

\frac{d}{d x} (1000 (1 + \frac{x}{12})^{60})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 1000 \frac{d}{d x} ((1 + \frac{x}{12})^{60})

Wende die Kettenregel an:

60 (1 + \frac{x}{12})^{59} \frac{d}{d x} (1 + \frac{x}{12})

= 60 (1 + \frac{x}{12})^{59} \frac{d}{d x} (1 + \frac{x}{12})

\frac{d}{d x} (1 + \frac{x}{12}) = \frac{1}{12}

= 1000 \cdot 60 (1 + \frac{x}{12})^{59} \frac{1}{12}

Vereinfache

1000 \cdot 60 (1 + \frac{x}{12})^{59} \frac{1}{12} : 5000 (\frac{x}{12} + 1)^{59}

= 5000 (\frac{x}{12} + 1)^{59}

d er i v a t i v e f (x) = (1 - x) (x^{2} - 7)^{2}

in v erse l a pl a ce \frac{10}{s ( s ^{2} + 8 s + 25 )}

\frac{\partial}{\partial x} (x arctan (yz))

x \to 0 lim (\frac{sin ( \frac{x}{2} )}{x})

x \to \infty lim ((1 + x)^{\frac{2}{x}})