derivative of ln^2(2*2^x-1/(x^2))

Lösung

\frac{d}{d x} (ln^{2} (2) \cdot 2^{x} - \frac{1}{x ^{2}})

ln^{3} (2) \cdot 2^{x} + \frac{2}{x ^{3}}

Schritte zur Lösung

\frac{d}{d x} (ln^{2} (2) \cdot 2^{x} - \frac{1}{x ^{2}})

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (ln^{2} (2) \cdot 2^{x}) - \frac{d}{d x} (\frac{1}{x ^{2}})

\frac{d}{d x} (ln^{2} (2) \cdot 2^{x}) = ln^{3} (2) \cdot 2^{x}

\frac{d}{d x} (\frac{1}{x ^{2}}) = - \frac{2}{x ^{3}}

= ln^{3} (2) \cdot 2^{x} - (- \frac{2}{x ^{3}})

Vereinfache

= ln^{3} (2) \cdot 2^{x} + \frac{2}{x ^{3}}

\int_{1}^{2} (\frac{1}{x} - \frac{1}{x ^{2}}) d x

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