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Beliebt Rechnen >

derivative of (-5/2 /(x^2)+5^x)

Lösung

\frac{d}{d x} (\frac{- \frac{5}{2}}{x ^{2}} + 5^{x})

Lösung

\frac{5}{x ^{3}} + ln (5) \cdot 5^{x}

Schritte zur Lösung

\frac{d}{d x} (\frac{- \frac{5}{2}}{x ^{2}} + 5^{x})

Vereinfache

\frac{- \frac{5}{2}}{x ^{2}} + 5^{x} : - \frac{5}{2 x ^{2}} + 5^{x}

= \frac{d}{d x} (- \frac{5}{2 x ^{2}} + 5^{x})

Wende die Summen-/Differenzregel an:

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

= - \frac{d}{d x} (\frac{5}{2 x ^{2}}) + \frac{d}{d x} (5^{x})

\frac{d}{d x} (\frac{5}{2 x ^{2}}) = - \frac{5}{x ^{3}}

\frac{d}{d x} (5^{x}) = 5^{x} ln (5)

= - (- \frac{5}{x ^{3}}) + 5^{x} ln (5)

Vereinfache

= \frac{5}{x ^{3}} + ln (5) \cdot 5^{x}

Graph

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