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Beliebt Rechnen >

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

Lösung

ableitung von

\frac{1}{4 x ^{2} + 5 x}

Lösung

- \frac{8 x + 5}{( 4 x ^{2} + 5 x ) ^{2}}

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (4 x^{2} + 5 x) = 8 x + 5

= - \frac{1}{( 4 x ^{2} + 5 x ) ^{2}} (8 x + 5)

Vereinfache

- \frac{1}{( 4 x ^{2} + 5 x ) ^{2}} (8 x + 5) : - \frac{8 x + 5}{( 4 x ^{2} + 5 x ) ^{2}}

= - \frac{8 x + 5}{( 4 x ^{2} + 5 x ) ^{2}}

Graph

Beliebte Beispiele

limit as x approaches infinity of \sqrt[3]{x^2}*e^{-x}

x \to \infty lim (3 x^{2} \cdot e^{- x})

tangent f(x)=8x^2-x^3,(1,7)

t an g e n t f (x) = 8 x^{2} - x^{3}, (1, 7)

taylor (x-5)^{7/3}

t a y l or (x - 5)^{\frac{7}{3}}

limit as x approaches 3 of 2/((x-3))

x \to 3 lim (\frac{2}{( x - 3 )})

steigung x^2+4x-1

s l o p e x^{2} + 4 x - 1