derivative of 0.01(0.2x^2+4x+64^{2/3})

解

\frac{d}{d x} (0.01 (0.2 x^{2} + 4 x + 64)^{\frac{2}{3}})

\frac{0.00666 \dots ( 0.4 x + 4 )}{( 0.2 x ^{2} + 4 x + 64 ) ^{\frac{1}{3}}}

解答ステップ

\frac{d}{d x} (0.01 (0.2 x^{2} + 4 x + 64)^{\frac{2}{3}})

定数を除去:

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

= 0.01 \frac{d}{d x} ((0.2 x^{2} + 4 x + 64)^{\frac{2}{3}})

連鎖法則を適用:

\frac{2}{3 ( 0.2 x ^{2} + 4 x + 64 ) ^{\frac{1}{3}}} \frac{d}{d x} (0.2 x^{2} + 4 x + 64)

= \frac{2}{3 ( 0.2 x ^{2} + 4 x + 64 ) ^{\frac{1}{3}}} \frac{d}{d x} (0.2 x^{2} + 4 x + 64)

\frac{d}{d x} (0.2 x^{2} + 4 x + 64) = 0.4 x + 4

= 0.01 \cdot \frac{2}{3 ( 0.2 x ^{2} + 4 x + 64 ) ^{\frac{1}{3}}} (0.4 x + 4)

簡素化

0.01 \cdot \frac{2}{3 ( 0.2 x ^{2} + 4 x + 64 ) ^{\frac{1}{3}}} (0.4 x + 4) : \frac{0.00666 \dots ( 0.4 x + 4 )}{( 0.2 x ^{2} + 4 x + 64 ) ^{\frac{1}{3}}}

= \frac{0.00666 \dots ( 0.4 x + 4 )}{( 0.2 x ^{2} + 4 x + 64 ) ^{\frac{1}{3}}}