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Beliebt Rechnen >

((16)/(x(4-x^2)))^'

Lösung

(\frac{16}{x ( 4 - x ^{2} )})^{^{'}}

Lösung

- \frac{16 ( 4 - 3 x ^{2} )}{x ^{2} ( 4 - x ^{2} ) ^{2}}

Schritte zur Lösung

(\frac{16}{x ( 4 - x ^{2} )})^{'}

Entferne die Konstante:

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

= 16 (\frac{1}{x ( 4 - x ^{2} )})^{^{'}}

Wende Exponentenregel an:

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

= 16 ((x (4 - x^{2}))^{- 1})^{^{'}}

Wende die Kettenregel an:

- \frac{1}{( x ( 4 - x ^{2} ) ) ^{2}} (x (4 - x^{2}))^{'}

= - \frac{1}{( x ( 4 - x ^{2} ) ) ^{2}} (x (4 - x^{2}))^{'}

(x (4 - x^{2}))^{'} = 4 - 3 x^{2}

= 16 (- \frac{1}{( x ( 4 - x ^{2} ) ) ^{2}} (4 - 3 x^{2}))

Vereinfache

16 (- \frac{1}{( x ( 4 - x ^{2} ) ) ^{2}} (4 - 3 x^{2})) : - \frac{16 ( 4 - 3 x ^{2} )}{x ^{2} ( 4 - x ^{2} ) ^{2}}

= - \frac{16 ( 4 - 3 x ^{2} )}{x ^{2} ( 4 - x ^{2} ) ^{2}}

Graph

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