derivative of 5/((6x+5^2))

Lösung

\frac{d}{d x} (\frac{5}{( 6 x + 5 ) ^{2}})

- \frac{60}{( 6 x + 5 ) ^{3}}

Schritte zur Lösung

\frac{d}{d x} (\frac{5}{( 6 x + 5 ) ^{2}})

Entferne die Konstante:

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

= 5 \frac{d}{d x} (\frac{1}{( 6 x + 5 ) ^{2}})

Wende Exponentenregel an:

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

= 5 \frac{d}{d x} ((6 x + 5)^{- 2})

Wende die Kettenregel an:

- \frac{2}{( 6 x + 5 ) ^{3}} \frac{d}{d x} (6 x + 5)

= - \frac{2}{( 6 x + 5 ) ^{3}} \frac{d}{d x} (6 x + 5)

\frac{d}{d x} (6 x + 5) = 6

= 5 (- \frac{2}{( 6 x + 5 ) ^{3}} \cdot 6)

Vereinfache

5 (- \frac{2}{( 6 x + 5 ) ^{3}} \cdot 6) : - \frac{60}{( 6 x + 5 ) ^{3}}

= - \frac{60}{( 6 x + 5 ) ^{3}}

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