d/(dy)(1/3 sqrt(y)(y-3))

解答

\frac{d}{d y} (\frac{1}{3} y (y - 3))

\frac{y - 1}{2 y}

求解步骤

\frac{d}{d y} (\frac{1}{3} y (y - 3))

将常数提出:

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

= \frac{1}{3} \frac{d}{d y} (y (y - 3))

使用微分乘法定则:

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

f = y, g = y - 3

= \frac{1}{3} (\frac{d}{d y} (y) (y - 3) + \frac{d}{d y} (y - 3) y)

\frac{d}{d y} (y) = \frac{1}{2 y}

\frac{d}{d y} (y - 3) = 1

= \frac{1}{3} (\frac{1}{2 y} (y - 3) + 1 \cdot y)

化简

\frac{1}{3} (\frac{1}{2 y} (y - 3) + 1 \cdot y) : \frac{y - 1}{2 y}

= \frac{y - 1}{2 y}

\frac{d}{d x} (x^{l n (x^{2} + 1)})

\frac{d ^{2}}{d x ^{2}} (e^{s i n (x)})

\frac{d}{d x} ((sin (y)) x^{2})

x \to 5 lim (h (x))

y^{^{'}} + 5 (tan (5 x)) y = - 8 (cos (5 x))