d/(dy)(y(2x+y^3))

解答

\frac{d}{d y} (y (2 x + y^{3}))

2 x + 4 y^{3}

求解步骤

\frac{d}{d y} (y (2 x + y^{3}))

将

x

视为常数

使用微分乘法定则:

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

f = y, g = 2 x + y^{3}

= \frac{d y}{d y} (2 x + y^{3}) + \frac{d}{d y} (2 x + y^{3}) y

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

\frac{d}{d y} (2 x + y^{3}) = 3 y^{2}

= 1 \cdot (2 x + y^{3}) + 3 y^{2} y

化简

1 \cdot (2 x + y^{3}) + 3 y^{2} y : 2 x + 4 y^{3}

= 2 x + 4 y^{3}

\int 2 sin (x) - tan (x) d x

\frac{\partial}{\partial x} (sin (π (4 x - y)))

\frac{d p}{2 ( p + 3 )} = \frac{d v}{- v}

x \to 0 + lim (x sin (x))

\int x^{2} x e^{x^{2}} d x