derivative-7/((x-7)^2)

解答

导数

- \frac{7}{( x - 7 ) ^{2}}

\frac{14}{( x - 7 ) ^{3}}

求解步骤

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

将常数提出:

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

= - 7 \frac{d}{d x} (\frac{1}{( x - 7 ) ^{2}})

使用指数法则:

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

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

使用连锁律:

- \frac{2}{( x - 7 ) ^{3}} \frac{d}{d x} (x - 7)

= - \frac{2}{( x - 7 ) ^{3}} \frac{d}{d x} (x - 7)

\frac{d}{d x} (x - 7) = 1

= - 7 (- \frac{2}{( x - 7 ) ^{3}} \cdot 1)

化简

- 7 (- \frac{2}{( x - 7 ) ^{3}} \cdot 1) : \frac{14}{( x - 7 ) ^{3}}

= \frac{14}{( x - 7 ) ^{3}}

\frac{\partial}{\partial y} (e^{x} - e^{x^{2}})

d er i v a t i v e 4 x^{2} + 9

\int (7 x + cos (x)) d x

\frac{d y}{d x} + \frac{2}{x} y = \frac{1}{x ^{2}}

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