d/(dt)((t)(k(M-t)))

解答

\frac{d}{d t} ((t) (k (M - t)))

k (M - 2 t)

求解步骤

\frac{d}{d t} ((t) (k (M - t)))

将

k, M

视为常数

将常数提出:

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

= k \frac{d}{d t} (t (M - t))

使用微分乘法定则:

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

f = t, g = M - t

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

\frac{d t}{d t} = 1

\frac{d}{d t} (M - t) = - 1

= k (1 \cdot (M - t) + (- 1) t)

化简

k (1 \cdot (M - t) + (- 1) t) : k (M - 2 t)

= k (M - 2 t)

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