derivative of ((x^2/(6-x))^5)

Lösung

\frac{d}{d x} ((\frac{x ^{2}}{6 - x})^{5})

\frac{5 x ^{8} ( 12 x - x ^{2} )}{( 6 - x ) ^{6}}

Schritte zur Lösung

\frac{d}{d x} ((\frac{x ^{2}}{6 - x})^{5})

Wende die Kettenregel an:

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

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

\frac{d}{d x} (\frac{x ^{2}}{6 - x}) = \frac{12 x - x ^{2}}{( 6 - x ) ^{2}}

= 5 (\frac{x ^{2}}{6 - x})^{4} \frac{12 x - x ^{2}}{( 6 - x ) ^{2}}

Vereinfache

5 (\frac{x ^{2}}{6 - x})^{4} \frac{12 x - x ^{2}}{( 6 - x ) ^{2}} : \frac{5 x ^{8} ( 12 x - x ^{2} )}{( 6 - x ) ^{6}}

= \frac{5 x ^{8} ( 12 x - x ^{2} )}{( 6 - x ) ^{6}}

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