derivative of (2x^2+x+9^{-3})

Lösung

\frac{d}{d x} ((2 x^{2} + x + 9)^{- 3})

- \frac{3 ( 4 x + 1 )}{( 2 x ^{2} + x + 9 ) ^{4}}

Schritte zur Lösung

\frac{d}{d x} ((2 x^{2} + x + 9)^{- 3})

Wende die Kettenregel an:

- \frac{3}{( 2 x ^{2} + x + 9 ) ^{4}} \frac{d}{d x} (2 x^{2} + x + 9)

= - \frac{3}{( 2 x ^{2} + x + 9 ) ^{4}} \frac{d}{d x} (2 x^{2} + x + 9)

\frac{d}{d x} (2 x^{2} + x + 9) = 4 x + 1

= - \frac{3}{( 2 x ^{2} + x + 9 ) ^{4}} (4 x + 1)

Multipliziere Brüche:

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

= - \frac{3 ( 4 x + 1 )}{( 2 x ^{2} + x + 9 ) ^{4}}

\int \frac{1 - x ^{2}}{x + x ^{3}} d x

\frac{d}{d x} (5 x^{3} + 7 x^{2.5} - 3 x + 1)

\int (\frac{4}{x} + \frac{x}{4}) d x

\frac{\partial}{\partial y} (5 x y)

ln (x) \frac{d y}{d x} = \frac{y}{x}