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

解

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

\frac{192 x ^{4} ( 4 x - x ^{2} )}{( 2 - x ) ^{4}}

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

3 (\frac{4 x ^{2}}{2 - x})^{2} \frac{4 ( 4 x - x ^{2} )}{( 2 - x ) ^{2}} : \frac{192 x ^{4} ( 4 x - x ^{2} )}{( 2 - x ) ^{4}}

= \frac{192 x ^{4} ( 4 x - x ^{2} )}{( 2 - x ) ^{4}}