derivative of ((-2x-1/(-4x+2))^5)

解答

\frac{d}{d x} ((\frac{- 2 x - 1}{- 4 x + 2})^{5})

- \frac{5 ( - 2 x - 1 ) ^{4}}{8 ( 2 x - 1 ) ^{6}}

求解步骤

\frac{d}{d x} ((\frac{- 2 x - 1}{- 4 x + 2})^{5})

使用连锁律:

5 (\frac{- 2 x - 1}{- 4 x + 2})^{4} \frac{d}{d x} (\frac{- 2 x - 1}{- 4 x + 2})

= 5 (\frac{- 2 x - 1}{- 4 x + 2})^{4} \frac{d}{d x} (\frac{- 2 x - 1}{- 4 x + 2})

\frac{d}{d x} (\frac{- 2 x - 1}{- 4 x + 2}) = - \frac{2}{( 2 x - 1 ) ^{2}}

= 5 (\frac{- 2 x - 1}{- 4 x + 2})^{4} (- \frac{2}{( 2 x - 1 ) ^{2}})

化简

5 (\frac{- 2 x - 1}{- 4 x + 2})^{4} (- \frac{2}{( 2 x - 1 ) ^{2}}) : - \frac{5 ( - 2 x - 1 ) ^{4}}{8 ( 2 x - 1 ) ^{6}}

= - \frac{5 ( - 2 x - 1 ) ^{4}}{8 ( 2 x - 1 ) ^{6}}

\int_{2}^{4} 2 x^{2} - 3 x + 1 d x

\frac{\partial}{\partial x} (cos (x ln (y)))

x \to + 0 + lim (\frac{36 - 4 x ^{2}}{x})

\int 2 x 2 x - 1 d x

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