derivative of (5x^2-2x+1^{-3})

Lösung

\frac{d}{d x} ((5 x^{2} - 2 x + 1)^{- 3})

- \frac{3 ( 10 x - 2 )}{( 5 x ^{2} - 2 x + 1 ) ^{4}}

Schritte zur Lösung

\frac{d}{d x} ((5 x^{2} - 2 x + 1)^{- 3})

Wende die Kettenregel an:

- \frac{3}{( 5 x ^{2} - 2 x + 1 ) ^{4}} \frac{d}{d x} (5 x^{2} - 2 x + 1)

= - \frac{3}{( 5 x ^{2} - 2 x + 1 ) ^{4}} \frac{d}{d x} (5 x^{2} - 2 x + 1)

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

= - \frac{3}{( 5 x ^{2} - 2 x + 1 ) ^{4}} (10 x - 2)

Multipliziere Brüche:

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

= - \frac{3 ( 10 x - 2 )}{( 5 x ^{2} - 2 x + 1 ) ^{4}}