derivative of (2x^2-5^{-12})

解

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

- \frac{48 x}{( 2 x ^{2} - 5 ) ^{13}}

解答ステップ

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

連鎖法則を適用:

- \frac{12}{( 2 x ^{2} - 5 ) ^{13}} \frac{d}{d x} (2 x^{2} - 5)

= - \frac{12}{( 2 x ^{2} - 5 ) ^{13}} \frac{d}{d x} (2 x^{2} - 5)

\frac{d}{d x} (2 x^{2} - 5) = 4 x

= - \frac{12}{( 2 x ^{2} - 5 ) ^{13}} \cdot 4 x

簡素化

- \frac{12}{( 2 x ^{2} - 5 ) ^{13}} \cdot 4 x : - \frac{48 x}{( 2 x ^{2} - 5 ) ^{13}}

= - \frac{48 x}{( 2 x ^{2} - 5 ) ^{13}}