derivative y=(5x^2-6x)^{-2}

Lösung

ableitung von

y = (5 x^{2} - 6 x)^{- 2}

- \frac{2 ( 10 x - 6 )}{( 5 x ^{2} - 6 x ) ^{3}}

Schritte zur Lösung

\frac{d}{d x} ((5 x^{2} - 6 x)^{- 2})

Wende die Kettenregel an:

- \frac{2}{( 5 x ^{2} - 6 x ) ^{3}} \frac{d}{d x} (5 x^{2} - 6 x)

= - \frac{2}{( 5 x ^{2} - 6 x ) ^{3}} \frac{d}{d x} (5 x^{2} - 6 x)

\frac{d}{d x} (5 x^{2} - 6 x) = 10 x - 6

= - \frac{2}{( 5 x ^{2} - 6 x ) ^{3}} (10 x - 6)

Multipliziere Brüche:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= - \frac{2 ( 10 x - 6 )}{( 5 x ^{2} - 6 x ) ^{3}}

\int \frac{sec ( x ) tan ( x )}{sec ( x ) - 6} d x

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