(\partial)/(\partial x)(x^6y^6+9x^4y)

解答

\frac{\partial}{\partial x} (x^{6} y^{6} + 9 x^{4} y)

6 y^{6} x^{5} + 36 y x^{3}

求解步骤

\frac{\partial}{\partial x} (x^{6} y^{6} + 9 x^{4} y)

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^{6} y^{6}) + \frac{\partial}{\partial x} (9 x^{4} y)

\frac{\partial}{\partial x} (x^{6} y^{6}) = 6 y^{6} x^{5}

\frac{\partial}{\partial x} (9 x^{4} y) = 36 y x^{3}

= 6 y^{6} x^{5} + 36 y x^{3}

s l o p e y = 2 x^{2} - 3 x, (2, 2)

x \to 2 - lim (\frac{x + 2}{x - 2})

d er i v a t i v e y = x - 2

x \to 1 lim (x^{2} + e^{x})

\frac{\partial}{\partial x} (5 x y arcsin (yz))