derivative (55.9)/(t^2-0.31t+11.2)

解答

导数

\frac{55.9}{t ^{2} - 0.31 t + 11.2}

- \frac{55.9 ( 2 t - 0.31 )}{( t ^{2} - 0.31 t + 11.2 ) ^{2}}

求解步骤

\frac{d}{d t} (\frac{55.9}{t ^{2} - 0.31 t + 11.2})

将常数提出:

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

= 55.9 \frac{d}{d t} (\frac{1}{t ^{2} - 0.31 t + 11.2})

使用指数法则:

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

= 55.9 \frac{d}{d t} ((t^{2} - 0.31 t + 11.2)^{- 1})

使用连锁律:

- \frac{1}{( t ^{2} - 0.31 t + 11.2 ) ^{2}} \frac{d}{d t} (t^{2} - 0.31 t + 11.2)

= - \frac{1}{( t ^{2} - 0.31 t + 11.2 ) ^{2}} \frac{d}{d t} (t^{2} - 0.31 t + 11.2)

\frac{d}{d t} (t^{2} - 0.31 t + 11.2) = 2 t - 0.31

= 55.9 (- \frac{1}{( t ^{2} - 0.31 t + 11.2 ) ^{2}} (2 t - 0.31))

化简

55.9 (- \frac{1}{( t ^{2} - 0.31 t + 11.2 ) ^{2}} (2 t - 0.31)) : - \frac{55.9 ( 2 t - 0.31 )}{( t ^{2} - 0.31 t + 11.2 ) ^{2}}

= - \frac{55.9 ( 2 t - 0.31 )}{( t ^{2} - 0.31 t + 11.2 ) ^{2}}

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