derivative of 5/(x-3)

Lösung

\frac{d}{d x} (\frac{5}{x - 3})

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

Schritte zur Lösung

\frac{d}{d x} (\frac{5}{x - 3})

Entferne die Konstante:

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

= 5 \frac{d}{d x} (\frac{1}{x - 3})

Wende Exponentenregel an:

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

= 5 \frac{d}{d x} ((x - 3)^{- 1})

Wende die Kettenregel an:

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

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

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

= 5 (- \frac{1}{( x - 3 ) ^{2}} \cdot 1)

Vereinfache

5 (- \frac{1}{( x - 3 ) ^{2}} \cdot 1) : - \frac{5}{( x - 3 ) ^{2}}

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

\int - 4 cos (x) d x

\int (5 x^{4} - 3 x^{2} + 2 x + 6) d x

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d er i v a t i v e sec^{2} (x) - 5