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Beliebt Rechnen >

derivative of 1/3 pix^2y

Lösung

\frac{d}{d x} (\frac{1}{3} π x^{2} y)

Lösung

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

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{3} π x^{2} y)

Entferne die Konstante:

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

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2}, g = y

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

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

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

Vereinfache

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

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

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