derivative of (4x^3+5^{3/2})

解

\frac{d}{d x} ((4 x^{3} + 5)^{\frac{3}{2}})

18 x^{2} (4 x^{3} + 5)^{\frac{1}{2}}

解答ステップ

\frac{d}{d x} ((4 x^{3} + 5)^{\frac{3}{2}})

連鎖法則を適用:

\frac{3 ( 4 x ^{3} + 5 ) ^{\frac{1}{2}}}{2} \frac{d}{d x} (4 x^{3} + 5)

= \frac{3 ( 4 x ^{3} + 5 ) ^{\frac{1}{2}}}{2} \frac{d}{d x} (4 x^{3} + 5)

\frac{d}{d x} (4 x^{3} + 5) = 12 x^{2}

= \frac{3 ( 4 x ^{3} + 5 ) ^{\frac{1}{2}}}{2} \cdot 12 x^{2}

簡素化

\frac{3 ( 4 x ^{3} + 5 ) ^{\frac{1}{2}}}{2} \cdot 12 x^{2} : 18 x^{2} (4 x^{3} + 5)^{\frac{1}{2}}

= 18 x^{2} (4 x^{3} + 5)^{\frac{1}{2}}