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

解答

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

6 y x^{2} + 3 y^{2}

求解步骤

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

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

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

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

= 6 y x^{2} + 3 y^{2}

\int 2 y^{\frac{3}{2}} d y

\int tan (8 x + 1) d x

\int \frac{3 arctan ( x )}{x ^{2}} d x

\frac{\partial}{\partial x} ((e^{x} - 2 x) cos (y))

\frac{d y}{d x} + a y - b = 0