derivative of 44(2x^3-5^{6/5})

解

\frac{d}{d x} (44 (2 x^{3} - 5)^{\frac{6}{5}})

\frac{1584 x ^{2} ( 2 x ^{3} - 5 ) ^{\frac{1}{5}}}{5}

解答ステップ

\frac{d}{d x} (44 (2 x^{3} - 5)^{\frac{6}{5}})

定数を除去:

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

= 44 \frac{d}{d x} ((2 x^{3} - 5)^{\frac{6}{5}})

連鎖法則を適用:

\frac{6 ( 2 x ^{3} - 5 ) ^{\frac{1}{5}}}{5} \frac{d}{d x} (2 x^{3} - 5)

= \frac{6 ( 2 x ^{3} - 5 ) ^{\frac{1}{5}}}{5} \frac{d}{d x} (2 x^{3} - 5)

\frac{d}{d x} (2 x^{3} - 5) = 6 x^{2}

= 44 \cdot \frac{6 ( 2 x ^{3} - 5 ) ^{\frac{1}{5}}}{5} \cdot 6 x^{2}

簡素化

44 \cdot \frac{6 ( 2 x ^{3} - 5 ) ^{\frac{1}{5}}}{5} \cdot 6 x^{2} : \frac{1584 x ^{2} ( 2 x ^{3} - 5 ) ^{\frac{1}{5}}}{5}

= \frac{1584 x ^{2} ( 2 x ^{3} - 5 ) ^{\frac{1}{5}}}{5}