derivative of 1/((x+3^2))

Lösung

\frac{d}{d x} (\frac{1}{( x + 3 ) ^{2}})

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

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{( x + 3 ) ^{2}})

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (x + 3) = 1

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

Vereinfache

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

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