derivative of (6x^3+7^{3/2})

解

\frac{d}{d x} ((6 x^{3} + 7)^{\frac{3}{2}})

27 x^{2} (6 x^{3} + 7)^{\frac{1}{2}}

解答ステップ

\frac{d}{d x} ((6 x^{3} + 7)^{\frac{3}{2}})

連鎖法則を適用:

\frac{3 ( 6 x ^{3} + 7 ) ^{\frac{1}{2}}}{2} \frac{d}{d x} (6 x^{3} + 7)

= \frac{3 ( 6 x ^{3} + 7 ) ^{\frac{1}{2}}}{2} \frac{d}{d x} (6 x^{3} + 7)

\frac{d}{d x} (6 x^{3} + 7) = 18 x^{2}

= \frac{3 ( 6 x ^{3} + 7 ) ^{\frac{1}{2}}}{2} \cdot 18 x^{2}

簡素化

\frac{3 ( 6 x ^{3} + 7 ) ^{\frac{1}{2}}}{2} \cdot 18 x^{2} : 27 x^{2} (6 x^{3} + 7)^{\frac{1}{2}}

= 27 x^{2} (6 x^{3} + 7)^{\frac{1}{2}}