d/(dt)(({Q}(t))k({Q}(t)-70))

解答

\frac{d}{d t} ((Q (t)) k (Q (t) - 70))

k (2 Q (t) \frac{d}{d t} (Q (t)) - 70 \frac{d}{d t} (Q (t)))

求解步骤

\frac{d}{d t} ((Q (t)) k (Q (t) - 70))

将常数提出:

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

= k \frac{d}{d t} (Q (t) (Q (t) - 70))

使用微分乘法定则:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = Q (t), g = Q (t) - 70

= k (\frac{d}{d t} (Q (t)) (Q (t) - 70) + \frac{d}{d t} (Q (t) - 70) Q (t))

\frac{d}{d t} (Q (t) - 70) = \frac{d}{d t} (Q (t))

= k (\frac{d}{d t} (Q (t)) (Q (t) - 70) + \frac{d}{d t} (Q (t)) Q (t))

乘开

\frac{d}{d t} (Q (t)) (Q (t) - 70) + \frac{d}{d t} (Q (t)) Q (t) : 2 Q (t) \frac{d}{d t} (Q (t)) - 70 \frac{d}{d t} (Q (t))

= k (2 Q (t) \frac{d}{d t} (Q (t)) - 70 \frac{d}{d t} (Q (t)))

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