derivative of (2x^2-4x^{1/2})

解

\frac{d}{d x} ((2 x^{2} - 4 x)^{\frac{1}{2}})

\frac{2 ( x - 1 )}{( 2 x ^{2} - 4 x ) ^{\frac{1}{2}}}

解答ステップ

\frac{d}{d x} ((2 x^{2} - 4 x)^{\frac{1}{2}})

連鎖法則を適用:

\frac{1}{2 ( 2 x ^{2} - 4 x ) ^{\frac{1}{2}}} \frac{d}{d x} (2 x^{2} - 4 x)

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

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

= \frac{1}{2 ( 2 x ^{2} - 4 x ) ^{\frac{1}{2}}} (4 x - 4)

簡素化

\frac{1}{2 ( 2 x ^{2} - 4 x ) ^{\frac{1}{2}}} (4 x - 4) : \frac{2 ( x - 1 )}{( 2 x ^{2} - 4 x ) ^{\frac{1}{2}}}

= \frac{2 ( x - 1 )}{( 2 x ^{2} - 4 x ) ^{\frac{1}{2}}}