derivative of 1/(5x^2+2x)

Lösung

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

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

in v erse l a pl a ce \frac{5 s + 3}{( s - 1 ) ( s ^{2} + 2 s + 5 )}

\frac{\partial}{\partial y} (x^{2} + e^{x y})

d er i v a t i v e y = csc^{1} (e^{8 t})

\int (x^{3} - 7 x) d x

\frac{\partial}{\partial x} (ln (x^{2} u))