d/(dy)(ky(1-y/N)(y/M-1))

解答

\frac{d}{d y} (k y (1 - \frac{y}{N}) (\frac{y}{M} - 1))

k (\frac{- 3 y ^{2} + 2 N y + 2 y M}{NM} - 1)

求解步骤

\frac{d}{d y} (k y (1 - \frac{y}{N}) (\frac{y}{M} - 1))

将

N, k, M

视为常数

将常数提出:

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

= k \frac{d}{d y} (y (1 - \frac{y}{N}) (\frac{y}{M} - 1))

使用微分乘法定则:

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

f = y, g = (1 - \frac{y}{N}) (\frac{y}{M} - 1)

= k (\frac{d y}{d y} (1 - \frac{y}{N}) (\frac{y}{M} - 1) + \frac{d}{d y} ((1 - \frac{y}{N}) (\frac{y}{M} - 1)) y)

\frac{d y}{d y} = 1

\frac{d}{d y} ((1 - \frac{y}{N}) (\frac{y}{M} - 1)) = \frac{- 2 y + N + M}{NM}

= k (1 \cdot (1 - \frac{y}{N}) (\frac{y}{M} - 1) + \frac{- 2 y + N + M}{NM} y)

化简

k (1 \cdot (1 - \frac{y}{N}) (\frac{y}{M} - 1) + \frac{- 2 y + N + M}{NM} y) : k (\frac{- 3 y ^{2} + 2 N y + 2 y M}{NM} - 1)

= k (\frac{- 3 y ^{2} + 2 N y + 2 y M}{NM} - 1)

\frac{d P}{d t} + P = 10, P (0) = 4

\frac{d y}{d x} = (- \frac{x}{y})

d er i v a t i v e \frac{1}{x ^{\frac{1}{2}}}

\int \frac{x ^{2}}{36 + x ^{2}} d x

d er i v a t i v e \frac{1}{6 x + 7}