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Beliebt Rechnen >

derivative of 3/(((56(2x-1)^7))-1/(((24)(2x-1)^6))-1/(((40(2x-1)^5))))

Lösung

\frac{d}{d x} \frac{3}{( ( 56 ) ( 2 x - 1 ) ^{7} )} - \frac{1}{( ( 24 ) ( 2 x - 1 ) ^{6} )} - \frac{1}{( ( 40 ( 2 x - 1 ) ^{5} ) )}

Lösung

\frac{x ^{2} - 1}{( 2 x - 1 ) ^{8}}

Schritte zur Lösung

\frac{d}{d x} \frac{3}{( ( 56 ) ( 2 x - 1 ) ^{7} )} - \frac{1}{( ( 24 ) ( 2 x - 1 ) ^{6} )} - \frac{1}{( ( 40 ( 2 x - 1 ) ^{5} ) )}

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{3}{56 ( 2 x - 1 ) ^{7}}) - \frac{d}{d x} (\frac{1}{24 ( 2 x - 1 ) ^{6}}) - \frac{d}{d x} (\frac{1}{40 ( 2 x - 1 ) ^{5}})

\frac{d}{d x} (\frac{3}{56 ( 2 x - 1 ) ^{7}}) = - \frac{3}{4 ( 2 x - 1 ) ^{8}}

\frac{d}{d x} (\frac{1}{24 ( 2 x - 1 ) ^{6}}) = - \frac{1}{2 ( 2 x - 1 ) ^{7}}

\frac{d}{d x} (\frac{1}{40 ( 2 x - 1 ) ^{5}}) = - \frac{1}{4 ( 2 x - 1 ) ^{6}}

= - \frac{3}{4 ( 2 x - 1 ) ^{8}} - (- \frac{1}{2 ( 2 x - 1 ) ^{7}}) - (- \frac{1}{4 ( 2 x - 1 ) ^{6}})

Vereinfache

- \frac{3}{4 ( 2 x - 1 ) ^{8}} - (- \frac{1}{2 ( 2 x - 1 ) ^{7}}) - (- \frac{1}{4 ( 2 x - 1 ) ^{6}}) : \frac{x ^{2} - 1}{( 2 x - 1 ) ^{8}}

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

Graph

Beliebte Beispiele

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