derivative of \sqrt[3]{(5x+pi^2^4})

解

\frac{d}{d x} (3 (5 x + π^{2})^{4})

\frac{20 ( 5 x + π ^{2} ) ^{\frac{1}{3}}}{3}

解答ステップ

\frac{d}{d x} (3 (5 x + π^{2})^{4})

連鎖法則を適用:

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

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

\frac{d}{d x} ((5 x + π^{2})^{4}) = 20 (5 x + π^{2})^{3}

= \frac{1}{3 ( ( 5 x + π ^{2} ) ^{4} ) ^{\frac{2}{3}}} \cdot 20 (5 x + π^{2})^{3}

簡素化

\frac{1}{3 ( ( 5 x + π ^{2} ) ^{4} ) ^{\frac{2}{3}}} \cdot 20 (5 x + π^{2})^{3} : \frac{20 ( 5 x + π ^{2} ) ^{\frac{1}{3}}}{3}

= \frac{20 ( 5 x + π ^{2} ) ^{\frac{1}{3}}}{3}