(\partial)/(\partial x)(4x^3y-6x^2y^2)

解答

\frac{\partial}{\partial x} (4 x^{3} y - 6 x^{2} y^{2})

12 y x^{2} - 12 y^{2} x

求解步骤

\frac{\partial}{\partial x} (4 x^{3} y - 6 x^{2} 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} (4 x^{3} y) - \frac{\partial}{\partial x} (6 x^{2} y^{2})

\frac{\partial}{\partial x} (4 x^{3} y) = 12 y x^{2}

\frac{\partial}{\partial x} (6 x^{2} y^{2}) = 12 y^{2} x

= 12 y x^{2} - 12 y^{2} x

\int 4 sin (2 x + 3) d x

y = e^{2 x} arcsin (x)

16 cos (2 x)

y - y^{^{''}} = (1 + π^{2}) sin (π x)

\int \frac{1}{1 + 11 x} d x