derivative of 73.3\sqrt[4]{x^3}

解

\frac{d}{d x} (73.3 4 x^{3})

\frac{54.975}{x ^{\frac{1}{4}}}

解答ステップ

\frac{d}{d x} (73.3 4 x^{3})

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= 73.3 \frac{d}{d x} (4 x^{3})

連鎖法則を適用:

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

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

\frac{d}{d x} (x^{3}) = 3 x^{2}

= 73.3 \cdot \frac{1}{4 ( x ^{3} ) ^{\frac{3}{4}}} \cdot 3 x^{2}

簡素化

73.3 \cdot \frac{1}{4 ( x ^{3} ) ^{\frac{3}{4}}} \cdot 3 x^{2} : \frac{54.975}{x ^{\frac{1}{4}}}

= \frac{54.975}{x ^{\frac{1}{4}}}