derivative g(x)= 1/(5x^2+4x)

Lösung

ableitung von

g (x) = \frac{1}{5 x ^{2} + 4 x}

- \frac{10 x + 4}{( 5 x ^{2} + 4 x ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{5 x ^{2} + 4 x})

Wende Exponentenregel an:

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

= \frac{d}{d x} ((5 x^{2} + 4 x)^{- 1})

Wende die Kettenregel an:

- \frac{1}{( 5 x ^{2} + 4 x ) ^{2}} \frac{d}{d x} (5 x^{2} + 4 x)

= - \frac{1}{( 5 x ^{2} + 4 x ) ^{2}} \frac{d}{d x} (5 x^{2} + 4 x)

\frac{d}{d x} (5 x^{2} + 4 x) = 10 x + 4

= - \frac{1}{( 5 x ^{2} + 4 x ) ^{2}} (10 x + 4)

Vereinfache

- \frac{1}{( 5 x ^{2} + 4 x ) ^{2}} (10 x + 4) : - \frac{10 x + 4}{( 5 x ^{2} + 4 x ) ^{2}}

= - \frac{10 x + 4}{( 5 x ^{2} + 4 x ) ^{2}}

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