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Beliebt Rechnen >

derivative of (a^2-x^3/(b^2))

Lösung

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

Lösung

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

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Summen-/Differenzregel an:

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

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

\frac{d}{d x} (a^{2}) = 0

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

= \frac{1}{b ^{2}} (0 - 3 x^{2})

Vereinfache

\frac{1}{b ^{2}} (0 - 3 x^{2}) : - \frac{3 x ^{2}}{b ^{2}}

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

Graph

Beliebte Beispiele

fläche x=7y^2,x=8+5y^2

a re a x = 7 y^{2}, x = 8 + 5 y^{2}

derivative (2x)/(x+2)

d er i v a t i v e \frac{2 x}{x + 2}

integral of (x^2+1)/(x^2)

\int \frac{x ^{2} + 1}{x ^{2}} d x

xe^ydy+(x^2+1)/y dx=0

x e^{y} d y + \frac{x ^{2} + 1}{y} d x = 0

derivative of sqrt((1-2x/(1+2x)))

\frac{d}{d x} (\frac{1 - 2 x}{1 + 2 x})