(\partial)/(\partial x)(x^5+3x^3y^2+3xy^4)

解答

\frac{\partial}{\partial x} (x^{5} + 3 x^{3} y^{2} + 3 x y^{4})

5 x^{4} + 9 y^{2} x^{2} + 3 y^{4}

求解步骤

\frac{\partial}{\partial x} (x^{5} + 3 x^{3} y^{2} + 3 x y^{4})

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} (x^{5}) + \frac{\partial}{\partial x} (3 x^{3} y^{2}) + \frac{\partial}{\partial x} (3 x y^{4})

\frac{\partial}{\partial x} (x^{5}) = 5 x^{4}

\frac{\partial}{\partial x} (3 x^{3} y^{2}) = 9 y^{2} x^{2}

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

= 5 x^{4} + 9 y^{2} x^{2} + 3 y^{4}

x \to 1 lim (\frac{x ^{2}}{x - 1})

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

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

\frac{d ^{2} y}{d x ^{2}} = 3

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