derivative of (-2/((x-1)^2))

解答

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

\frac{4}{( x - 1 ) ^{3}}

求解步骤

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

化简

\frac{- 2}{( x - 1 ) ^{2}} : - \frac{2}{( x - 1 ) ^{2}}

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

将常数提出:

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

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

使用指数法则:

\frac{1}{a} = a^{- 1}

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

使用连锁律:

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

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

\frac{d}{d x} (x - 1) = 1

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

化简

- 2 (- \frac{2}{( x - 1 ) ^{3}} \cdot 1) : \frac{4}{( x - 1 ) ^{3}}

= \frac{4}{( x - 1 ) ^{3}}

y^{^{'}} = e^{5 x} - 9 x

\frac{\partial}{\partial x} (y + 2)

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

\int_{0}^{r} r^{2} - x^{2} d x

\frac{d}{d x} (3 x^{4} - 4 x^{3})