derivative of (-11/((x-3)^2))

解答

\frac{d}{d x} (\frac{- 11}{( x - 3 ) ^{2}})

\frac{22}{( x - 3 ) ^{3}}

求解步骤

\frac{d}{d x} (\frac{- 11}{( x - 3 ) ^{2}})

化简

\frac{- 11}{( x - 3 ) ^{2}} : - \frac{11}{( x - 3 ) ^{2}}

= \frac{d}{d x} (- \frac{11}{( x - 3 ) ^{2}})

将常数提出:

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

= - 11 \frac{d}{d x} (\frac{1}{( x - 3 ) ^{2}})

使用指数法则:

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

= - 11 \frac{d}{d x} ((x - 3)^{- 2})

使用连锁律:

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

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

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

= - 11 (- \frac{2}{( x - 3 ) ^{3}} \cdot 1)

化简

- 11 (- \frac{2}{( x - 3 ) ^{3}} \cdot 1) : \frac{22}{( x - 3 ) ^{3}}

= \frac{22}{( x - 3 ) ^{3}}