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Beliebt Rechnen >

derivative of (1/2 x^2-3^2)

Lösung

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

Lösung

x^{3} - 6 x

Schritte zur Lösung

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

Vereinfache

(\frac{1}{2} x^{2} - 3)^{2} : \frac{x ^{4}}{4} - 3 x^{2} + 9

= \frac{d}{d x} (\frac{x ^{4}}{4} - 3 x^{2} + 9)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (\frac{x ^{4}}{4}) - \frac{d}{d x} (3 x^{2}) + \frac{d}{d x} (9)

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

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

\frac{d}{d x} (9) = 0

= x^{3} - 6 x + 0

Vereinfache

= x^{3} - 6 x

Graph

Beliebte Beispiele

(d^2}{dx^2}(\frac{ln(x))/x)

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

derivative of 2+e^x

\frac{d}{d x} (2 + e^{x})

limit as x approaches 3 of 10^{x^2-4x}

x \to 3 lim (1 0^{x^{2} - 4 x})

t y^{^{'}} - y = 0

fläche ln(x),y=2,1,e^2

a re a ln (x), y = 2, 1, e^{2}