derivative f(x)=7+2/x+5/(x^2)

Lösung

ableitung von

f (x) = 7 + \frac{2}{x} + \frac{5}{x ^{2}}

- \frac{2}{x ^{2}} - \frac{10}{x ^{3}}

Schritte zur Lösung

\frac{d}{d x} (7 + \frac{2}{x} + \frac{5}{x ^{2}})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (7) + \frac{d}{d x} (\frac{2}{x}) + \frac{d}{d x} (\frac{5}{x ^{2}})

\frac{d}{d x} (7) = 0

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

\frac{d}{d x} (\frac{5}{x ^{2}}) = - \frac{10}{x ^{3}}

= 0 - \frac{2}{x ^{2}} - \frac{10}{x ^{3}}

Vereinfache

= - \frac{2}{x ^{2}} - \frac{10}{x ^{3}}

\int \frac{1}{( x - 9 ) ( 3 - x )} d x

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d er i v a t i v e y = (3 x^{2} + 2) (4 x - 1)

\frac{d}{d x} (\frac{e ^{x}}{x ^{2}})