derivative (5x^2-x+11)^{3/2}

解

導関数

(5 x^{2} - x + 11)^{\frac{3}{2}}

\frac{3 ( 10 x - 1 ) ( 5 x ^{2} - x + 11 ) ^{\frac{1}{2}}}{2}

解答ステップ

\frac{d}{d x} ((5 x^{2} - x + 11)^{\frac{3}{2}})

連鎖法則を適用:

\frac{3 ( 5 x ^{2} - x + 11 ) ^{\frac{1}{2}}}{2} \frac{d}{d x} (5 x^{2} - x + 11)

= \frac{3 ( 5 x ^{2} - x + 11 ) ^{\frac{1}{2}}}{2} \frac{d}{d x} (5 x^{2} - x + 11)

\frac{d}{d x} (5 x^{2} - x + 11) = 10 x - 1

= \frac{3 ( 5 x ^{2} - x + 11 ) ^{\frac{1}{2}}}{2} (10 x - 1)

分数を乗じる:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{3 ( 10 x - 1 ) ( 5 x ^{2} - x + 11 ) ^{\frac{1}{2}}}{2}