derivative of 1/(5-2x)

Lösung

\frac{d}{d x} (\frac{1}{5 - 2 x})

\frac{2}{( 5 - 2 x ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{5 - 2 x})

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

- \frac{1}{( 5 - 2 x ) ^{2}} \frac{d}{d x} (5 - 2 x)

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

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

= - \frac{1}{( 5 - 2 x ) ^{2}} (- 2)

Vereinfache

- \frac{1}{( 5 - 2 x ) ^{2}} (- 2) : \frac{2}{( 5 - 2 x ) ^{2}}

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

\int \frac{9 - 162 x}{64 - 81 x ^{2}} d x

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