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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

integral of cos(x)cos(sin(x))

\int cos (x) cos (sin (x)) d x

limit as x approaches+5-of 5/((x-5)^3)

x \to + 5 - lim (\frac{5}{( x - 5 ) ^{3}})

integral of ((3x+5)^3)/(10)

\int \frac{( 3 x + 5 ) ^{3}}{10} d x

(\partial)/(\partial x)(10990+1120x+873y)

\frac{\partial}{\partial x} (10990 + 1120 x + 873 y)

tangent sqrt(5x+1)

t an g e n t 5 x + 1