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Beliebt Rechnen >

derivative of (x^3-2xsqrt(x)/x)

Lösung

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

Lösung

2 x - \frac{1}{x}

Schritte zur Lösung

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

Vereinfache

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

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

Wende die Summen-/Differenzregel an:

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

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

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

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

= 2 x - \frac{1}{x}

Graph

Beliebte Beispiele

steigung (0,-9),(7,6)

s l o p e (0, - 9), (7, 6)

tangent f(x)=x(x^2-4x+5)^5,\at x=2

t an g e n t f (x) = x (x^{2} - 4 x + 5)^{5}, at x = 2

x*y^'=2y+e^x*x^3

x \cdot y^{^{'}} = 2 y + e^{x} \cdot x^{3}

limit as x approaches-1/2 of 7/(2x+1)

x \to - \frac{1}{2} lim (\frac{7}{2 x + 1})

fläche-x^2+2x,3x^3-x^2-10x

a re a - x^{2} + 2 x, 3 x^{3} - x^{2} - 10 x