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Beliebt Rechnen >

derivative g(x)= 1/(5x^2+2x)

Lösung

ableitung von

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

Lösung

- \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}}

Graph

Beliebte Beispiele

y^{''}+5y^'+6.25y=0

y^{^{''}} + 5 y^{^{'}} + 6.25 y = 0

derivative of 5x-2x^2

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

integral from 1 to 4 of x^{1/2}ln(x)

\int_{1}^{4} x^{\frac{1}{2}} ln (x) d x

inverselaplace 1/(s+40)

in v erse l a pl a ce \frac{1}{s + 40}

integral of 1/(2x+7)

\int \frac{1}{2 x + 7} d x