(\partial)/(\partial x)(3x+4y^2+3x^2y^3)

解答

\frac{\partial}{\partial x} (3 x + 4 y^{2} + 3 x^{2} y^{3})

6 x y^{3} + 3

求解步骤

\frac{\partial}{\partial x} (3 x + 4 y^{2} + 3 x^{2} y^{3})

将

y

视为常数

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (3 x) + \frac{\partial}{\partial x} (4 y^{2}) + \frac{\partial}{\partial x} (3 x^{2} y^{3})

\frac{\partial}{\partial x} (3 x) = 3

\frac{\partial}{\partial x} (4 y^{2}) = 0

\frac{\partial}{\partial x} (3 x^{2} y^{3}) = 6 y^{3} x

= 3 + 0 + 6 y^{3} x

化简

= 6 x y^{3} + 3

\int x - 2 π d x

\int (x) \frac{3}{4} x^{2} - 4 x + 8 d x

\frac{d}{d x} ((2 x^{3}) (4 x^{2}))

s l o p e in t erce pt (0, 5), (- 1.5, 1)

2 t \frac{d y}{d t} - 4 y = t