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Beliebt Rechnen >

d/(dy)(1/3 sqrt(y)(y-3))

Lösung

\frac{d}{d y} (\frac{1}{3} y (y - 3))

Lösung

\frac{y - 1}{2 y}

Schritte zur Lösung

\frac{d}{d y} (\frac{1}{3} y (y - 3))

Entferne die Konstante:

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

= \frac{1}{3} \frac{d}{d y} (y (y - 3))

Wende die Produktregel an:

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

f = y, g = y - 3

= \frac{1}{3} (\frac{d}{d y} (y) (y - 3) + \frac{d}{d y} (y - 3) y)

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

\frac{d}{d y} (y - 3) = 1

= \frac{1}{3} (\frac{1}{2 y} (y - 3) + 1 \cdot y)

Vereinfache

\frac{1}{3} (\frac{1}{2 y} (y - 3) + 1 \cdot y) : \frac{y - 1}{2 y}

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

Graph

Beliebte Beispiele

derivative of x^{ln(x^2+1})

(d^2)/(dx^2)(e^{sin(x)})

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limit as x approaches 5 of h(x)

y^'+5(tan(5x))y=-8(cos(5x))