derivative of-7sqrt(x^3)-2/(x^3+7x)

Lösung

\frac{d}{d x} (- 7 x^{3} - \frac{2}{x ^{3}} + 7 x)

- \frac{21 x}{2} + \frac{6}{x ^{4}} + 7

Schritte zur Lösung

\frac{d}{d x} (- 7 x^{3} - \frac{2}{x ^{3}} + 7 x)

Wende die Summen-/Differenzregel an:

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

= - \frac{d}{d x} (7 x^{3}) - \frac{d}{d x} (\frac{2}{x ^{3}}) + \frac{d}{d x} (7 x)

\frac{d}{d x} (7 x^{3}) = \frac{21 x}{2}

\frac{d}{d x} (\frac{2}{x ^{3}}) = - \frac{6}{x ^{4}}

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

= - \frac{21 x}{2} - (- \frac{6}{x ^{4}}) + 7

Vereinfache

= - \frac{21 x}{2} + \frac{6}{x ^{4}} + 7

\int \frac{1}{25 x ^{2} - 81} d x

y^{^{'}} - y^{2} = 0

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\frac{\partial}{\partial x} (4 + ln (x y - 5))