derivative f(x)=sqrt((5-2x)(3x-1)^3)

解

導関数

f (x) = (5 - 2 x) (3 x - 1)^{3}

\frac{( - 24 x + 47 ) ( 3 x - 1 ) ^{\frac{3}{2}}}{2 ( 3 x - 1 ) ^{2} - 2 x + 5}

解答ステップ

\frac{d}{d x} ((5 - 2 x) (3 x - 1)^{3})

連鎖法則を適用:

\frac{1}{2 ( 5 - 2 x ) ( 3 x - 1 ) ^{3}} \frac{d}{d x} ((5 - 2 x) (3 x - 1)^{3})

= \frac{1}{2 ( 5 - 2 x ) ( 3 x - 1 ) ^{3}} \frac{d}{d x} ((5 - 2 x) (3 x - 1)^{3})

\frac{d}{d x} ((5 - 2 x) (3 x - 1)^{3}) = - 2 (3 x - 1)^{3} + 9 (3 x - 1)^{2} (5 - 2 x)

= \frac{1}{2 ( 5 - 2 x ) ( 3 x - 1 ) ^{3}} (- 2 (3 x - 1)^{3} + 9 (3 x - 1)^{2} (5 - 2 x))

簡素化

\frac{1}{2 ( 5 - 2 x ) ( 3 x - 1 ) ^{3}} (- 2 (3 x - 1)^{3} + 9 (3 x - 1)^{2} (5 - 2 x)) : \frac{( - 24 x + 47 ) ( 3 x - 1 ) ^{\frac{3}{2}}}{2 ( 3 x - 1 ) ^{2} - 2 x + 5}

= \frac{( - 24 x + 47 ) ( 3 x - 1 ) ^{\frac{3}{2}}}{2 ( 3 x - 1 ) ^{2} - 2 x + 5}