derivative of 2(x^2+5x-2^{-5/7})

解

\frac{d}{d x} (2 (x^{2} + 5 x - 2)^{- \frac{5}{7}})

- \frac{10 ( 2 x + 5 )}{7 ( x ^{2} + 5 x - 2 ) ^{\frac{12}{7}}}

解答ステップ

\frac{d}{d x} (2 (x^{2} + 5 x - 2)^{- \frac{5}{7}})

定数を除去:

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

= 2 \frac{d}{d x} ((x^{2} + 5 x - 2)^{- \frac{5}{7}})

連鎖法則を適用:

- \frac{5}{7 ( x ^{2} + 5 x - 2 ) ^{\frac{12}{7}}} \frac{d}{d x} (x^{2} + 5 x - 2)

= - \frac{5}{7 ( x ^{2} + 5 x - 2 ) ^{\frac{12}{7}}} \frac{d}{d x} (x^{2} + 5 x - 2)

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

= 2 (- \frac{5}{7 ( x ^{2} + 5 x - 2 ) ^{\frac{12}{7}}} (2 x + 5))

簡素化

2 (- \frac{5}{7 ( x ^{2} + 5 x - 2 ) ^{\frac{12}{7}}} (2 x + 5)) : - \frac{10 ( 2 x + 5 )}{7 ( x ^{2} + 5 x - 2 ) ^{\frac{12}{7}}}

= - \frac{10 ( 2 x + 5 )}{7 ( x ^{2} + 5 x - 2 ) ^{\frac{12}{7}}}