derivative of 1/(1+3x)

Lösung

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

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\int_{1}^{e} ln (x^{2}) d x

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