derivative y=-7/((t+5)^2)

解答

导数

y = - \frac{7}{( t + 5 ) ^{2}}

\frac{14}{( t + 5 ) ^{3}}

求解步骤

\frac{d}{d t} (- \frac{7}{( t + 5 ) ^{2}})

将常数提出:

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

= - 7 \frac{d}{d t} (\frac{1}{( t + 5 ) ^{2}})

使用指数法则:

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

= - 7 \frac{d}{d t} ((t + 5)^{- 2})

使用连锁律:

- \frac{2}{( t + 5 ) ^{3}} \frac{d}{d t} (t + 5)

= - \frac{2}{( t + 5 ) ^{3}} \frac{d}{d t} (t + 5)

\frac{d}{d t} (t + 5) = 1

= - 7 (- \frac{2}{( t + 5 ) ^{3}} \cdot 1)

化简

- 7 (- \frac{2}{( t + 5 ) ^{3}} \cdot 1) : \frac{14}{( t + 5 ) ^{3}}

= \frac{14}{( t + 5 ) ^{3}}

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