derivative y=(4x-3)^{1/2}

解

導関数

y = (4 x - 3)^{\frac{1}{2}}

\frac{2}{( 4 x - 3 ) ^{\frac{1}{2}}}

解答ステップ

\frac{d}{d x} ((4 x - 3)^{\frac{1}{2}})

連鎖法則を適用:

\frac{1}{2 ( 4 x - 3 ) ^{\frac{1}{2}}} \frac{d}{d x} (4 x - 3)

= \frac{1}{2 ( 4 x - 3 ) ^{\frac{1}{2}}} \frac{d}{d x} (4 x - 3)

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

= \frac{1}{2 ( 4 x - 3 ) ^{\frac{1}{2}}} \cdot 4

簡素化

\frac{1}{2 ( 4 x - 3 ) ^{\frac{1}{2}}} \cdot 4 : \frac{2}{( 4 x - 3 ) ^{\frac{1}{2}}}

= \frac{2}{( 4 x - 3 ) ^{\frac{1}{2}}}