(\partial)/(\partial x)((3x^2+5x+1)^{3/2})

解

\frac{\partial}{\partial x} ((3 x^{2} + 5 x + 1)^{\frac{3}{2}})

\frac{3 ( 6 x + 5 ) ( 3 x ^{2} + 5 x + 1 ) ^{\frac{1}{2}}}{2}

解答ステップ

\frac{\partial}{\partial x} ((3 x^{2} + 5 x + 1)^{\frac{3}{2}})

連鎖法則を適用:

\frac{3 ( 3 x ^{2} + 5 x + 1 ) ^{\frac{1}{2}}}{2} \frac{\partial}{\partial x} (3 x^{2} + 5 x + 1)

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

\frac{\partial}{\partial x} (3 x^{2} + 5 x + 1) = 6 x + 5

= \frac{3 ( 3 x ^{2} + 5 x + 1 ) ^{\frac{1}{2}}}{2} (6 x + 5)

分数を乗じる:

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

= \frac{3 ( 6 x + 5 ) ( 3 x ^{2} + 5 x + 1 ) ^{\frac{1}{2}}}{2}