derivative of (x^2}{100}+8+\frac{20/x)

Lösung

\frac{d}{d x} (\frac{x ^{2}}{100} + 8 + \frac{20}{x})

\frac{x}{50} - \frac{20}{x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{2}}{100} + 8 + \frac{20}{x})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (\frac{x ^{2}}{100}) + \frac{d}{d x} (8) + \frac{d}{d x} (\frac{20}{x})

\frac{d}{d x} (\frac{x ^{2}}{100}) = \frac{x}{50}

\frac{d}{d x} (8) = 0

\frac{d}{d x} (\frac{20}{x}) = - \frac{20}{x ^{2}}

= \frac{x}{50} + 0 - \frac{20}{x ^{2}}

Vereinfache

= \frac{x}{50} - \frac{20}{x ^{2}}

\frac{d}{d x} (cos (x) - 6 tan (x))

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