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Beliebt Rechnen >

derivative ((4-80y)/y)(y-48)

Lösung

ableitung von

(\frac{4 - 80 y}{y}) (y - 48)

Lösung

\frac{- 80 y ^{2} + 192}{y ^{2}}

Schritte zur Lösung

\frac{d}{d y} (\frac{4 - 80 y}{y} (y - 48))

Wende die Produktregel an:

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

f = \frac{4 - 80 y}{y}, g = y - 48

= \frac{d}{d y} (\frac{4 - 80 y}{y}) (y - 48) + \frac{d}{d y} (y - 48) \frac{4 - 80 y}{y}

\frac{d}{d y} (\frac{4 - 80 y}{y}) = - \frac{4}{y ^{2}}

\frac{d}{d y} (y - 48) = 1

= (- \frac{4}{y ^{2}}) (y - 48) + 1 \cdot \frac{4 - 80 y}{y}

Vereinfache

(- \frac{4}{y ^{2}}) (y - 48) + 1 \cdot \frac{4 - 80 y}{y} : \frac{- 80 y ^{2} + 192}{y ^{2}}

= \frac{- 80 y ^{2} + 192}{y ^{2}}

Graph

Beliebte Beispiele

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fläche y=1-x^2,y=4-4x

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