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Beliebt Rechnen >

derivative of 1/3 x^3-5x-4/x

Lösung

\frac{d}{d x} (\frac{1}{3} x^{3} - 5 x - \frac{4}{x})

Lösung

x^{2} - 5 + \frac{4}{x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{3} x^{3} - 5 x - \frac{4}{x})

Vereinfache

\frac{1}{3} x^{3} - 5 x - \frac{4}{x} : \frac{x ^{3}}{3} - 5 x - \frac{4}{x}

= \frac{d}{d x} (\frac{x ^{3}}{3} - 5 x - \frac{4}{x})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (\frac{x ^{3}}{3}) - \frac{d}{d x} (5 x) - \frac{d}{d x} (\frac{4}{x})

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

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

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

= x^{2} - 5 - (- \frac{4}{x ^{2}})

Vereinfache

= x^{2} - 5 + \frac{4}{x ^{2}}

Graph

Beliebte Beispiele

integral of x*ln^5(x)

\int x \cdot ln^{5} (x) d x

y^{''}-4y^'+4y=e^x+xe^{2x}

y^{^{''}} - 4 y^{^{'}} + 4 y = e^{x} + x e^{2 x}

f (x) = cot (x^{2})

integral from-1 to 0 of x^3-x^2-2x

\int_{- 1}^{0} x^{3} - x^{2} - 2 x d x

integral of x^4cos(2x)

\int x^{4} cos (2 x) d x