derivative y=((8x^2-5)/(2-x))^3

Lösung

ableitung von

y = (\frac{8 x ^{2} - 5}{2 - x})^{3}

\frac{3 ( 8 x ^{2} - 5 ) ^{2} ( 32 x - 8 x ^{2} - 5 )}{( 2 - x ) ^{4}}

Schritte zur Lösung

\frac{d}{d x} ((\frac{8 x ^{2} - 5}{2 - x})^{3})

Wende die Kettenregel an:

3 (\frac{8 x ^{2} - 5}{2 - x})^{2} \frac{d}{d x} (\frac{8 x ^{2} - 5}{2 - x})

= 3 (\frac{8 x ^{2} - 5}{2 - x})^{2} \frac{d}{d x} (\frac{8 x ^{2} - 5}{2 - x})

\frac{d}{d x} (\frac{8 x ^{2} - 5}{2 - x}) = \frac{32 x - 8 x ^{2} - 5}{( 2 - x ) ^{2}}

= 3 (\frac{8 x ^{2} - 5}{2 - x})^{2} \frac{32 x - 8 x ^{2} - 5}{( 2 - x ) ^{2}}

Vereinfache

3 (\frac{8 x ^{2} - 5}{2 - x})^{2} \frac{32 x - 8 x ^{2} - 5}{( 2 - x ) ^{2}} : \frac{3 ( 8 x ^{2} - 5 ) ^{2} ( 32 x - 8 x ^{2} - 5 )}{( 2 - x ) ^{4}}

= \frac{3 ( 8 x ^{2} - 5 ) ^{2} ( 32 x - 8 x ^{2} - 5 )}{( 2 - x ) ^{4}}

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