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Beliebt Rechnen >

derivative of (150000/((4x+75)^2))

Lösung

\frac{d}{d x} (\frac{150000}{( 4 x + 75 ) ^{2}})

Lösung

- \frac{1200000}{( 4 x + 75 ) ^{3}}

Schritte zur Lösung

\frac{d}{d x} (\frac{150000}{( 4 x + 75 ) ^{2}})

Entferne die Konstante:

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

= 150000 \frac{d}{d x} (\frac{1}{( 4 x + 75 ) ^{2}})

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

= 150000 \frac{d}{d x} ((4 x + 75)^{- 2})

Wende die Kettenregel an:

- \frac{2}{( 4 x + 75 ) ^{3}} \frac{d}{d x} (4 x + 75)

= - \frac{2}{( 4 x + 75 ) ^{3}} \frac{d}{d x} (4 x + 75)

\frac{d}{d x} (4 x + 75) = 4

= 150000 (- \frac{2}{( 4 x + 75 ) ^{3}} \cdot 4)

Vereinfache

150000 (- \frac{2}{( 4 x + 75 ) ^{3}} \cdot 4) : - \frac{1200000}{( 4 x + 75 ) ^{3}}

= - \frac{1200000}{( 4 x + 75 ) ^{3}}

Graph

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