derivative of ((8x^2/(4-x))^3)

Lösung

\frac{d}{d x} ((\frac{8 x ^{2}}{4 - x})^{3})

\frac{1536 x ^{4} ( 8 x - x ^{2} )}{( 4 - x ) ^{4}}

Schritte zur Lösung

\frac{d}{d x} ((\frac{8 x ^{2}}{4 - x})^{3})

Wende die Kettenregel an:

3 (\frac{8 x ^{2}}{4 - x})^{2} \frac{d}{d x} (\frac{8 x ^{2}}{4 - x})

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

\frac{d}{d x} (\frac{8 x ^{2}}{4 - x}) = \frac{8 ( 8 x - x ^{2} )}{( 4 - x ) ^{2}}

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

Vereinfache

3 (\frac{8 x ^{2}}{4 - x})^{2} \frac{8 ( 8 x - x ^{2} )}{( 4 - x ) ^{2}} : \frac{1536 x ^{4} ( 8 x - x ^{2} )}{( 4 - x ) ^{4}}

= \frac{1536 x ^{4} ( 8 x - x ^{2} )}{( 4 - x ) ^{4}}

\frac{d}{d x} (4 x^{3} + 3 x^{2} - 6 x)

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