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Beliebt Rechnen >

derivative of \sqrt[3]{x}-(10/x)

Lösung

\frac{d}{d x} (3 x - \frac{10}{x})

Lösung

\frac{x ^{2} + 30 x ^{\frac{2}{3}}}{3 x ^{\frac{8}{3}}}

Schritte zur Lösung

\frac{d}{d x} (3 x - \frac{10}{x})

Wende die Summen-/Differenzregel an:

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

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

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

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

= \frac{1}{3 x ^{\frac{2}{3}}} - (- \frac{10}{x ^{2}})

Vereinfache

\frac{1}{3 x ^{\frac{2}{3}}} - (- \frac{10}{x ^{2}}) : \frac{x ^{2} + 30 x ^{\frac{2}{3}}}{3 x ^{\frac{8}{3}}}

= \frac{x ^{2} + 30 x ^{\frac{2}{3}}}{3 x ^{\frac{8}{3}}}

Graph

Beliebte Beispiele

derivative of x(x^2+1^3)

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

(\partial)/(\partial x)(8x^2y+5xy^3)

\frac{\partial}{\partial x} (8 x^{2} y + 5 x y^{3})

tangent y=7x^2-4x,-74

t an g e n t y = 7 x^{2} - 4 x, - 74

integral of (x-9)^2

\int (x - 9)^{2} d x

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\int_{0}^{\frac{π}{3}} tan^{5} (x) d x