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

解答

导数

f (x) = - \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}}

\int sin^{2} (\frac{2 π x}{L}) d x

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

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

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