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Beliebt Rechnen >

(\partial)/(\partial x)(4/((x+2)^2))

Lösung

\frac{\partial}{\partial x} (\frac{4}{( x + 2 ) ^{2}})

Lösung

- \frac{8}{( x + 2 ) ^{3}}

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{4}{( x + 2 ) ^{2}})

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

\frac{\partial}{\partial x} (x + 2) = 1

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

Vereinfache

4 (- \frac{2}{( x + 2 ) ^{3}} \cdot 1) : - \frac{8}{( x + 2 ) ^{3}}

= - \frac{8}{( x + 2 ) ^{3}}

Beliebte Beispiele

t a y l or \frac{4}{x}, 3

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\int x (x^{2} + 3)^{100} d x