derivative of 17.5(x+1^{0.75})

Lösung

\frac{d}{d x} (17.5 (x + 1)^{0.75})

\frac{13.125}{( x + 1 ) ^{0.25}}

Schritte zur Lösung

\frac{d}{d x} (17.5 (x + 1)^{0.75})

Entferne die Konstante:

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

= 17.5 \frac{d}{d x} ((x + 1)^{0.75})

Wende die Kettenregel an:

\frac{0.75}{( x + 1 ) ^{0.25}} \frac{d}{d x} (x + 1)

= \frac{0.75}{( x + 1 ) ^{0.25}} \frac{d}{d x} (x + 1)

\frac{d}{d x} (x + 1) = 1

= 17.5 \cdot \frac{0.75}{( x + 1 ) ^{0.25}} \cdot 1

Vereinfache

17.5 \cdot \frac{0.75}{( x + 1 ) ^{0.25}} \cdot 1 : \frac{13.125}{( x + 1 ) ^{0.25}}

= \frac{13.125}{( x + 1 ) ^{0.25}}

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