derivative of e^{x^2*\sqrt[3]{4x-1}}

解

\frac{d}{d x} (e^{x^{2} \cdot 3 4 x - 1})

e^{x^{2} 3 4 x - 1} (2 x 3 4 x - 1 + \frac{4 x ^{2}}{3 ( 4 x - 1 ) ^{\frac{2}{3}}})

解答ステップ

\frac{d}{d x} (e^{x^{2} 3 4 x - 1})

連鎖法則を適用:

e^{x^{2} 3 4 x - 1} \frac{d}{d x} (x^{2} 3 4 x - 1)

= e^{x^{2} 3 4 x - 1} \frac{d}{d x} (x^{2} 3 4 x - 1)

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

= e^{x^{2} 3 4 x - 1} (2 x 3 4 x - 1 + \frac{4 x ^{2}}{3 ( 4 x - 1 ) ^{\frac{2}{3}}})