(\partial)/(\partial x)(x^8y^6+3x^7y)

解答

\frac{\partial}{\partial x} (x^{8} y^{6} + 3 x^{7} y)

8 y^{6} x^{7} + 21 y x^{6}

求解步骤

\frac{\partial}{\partial x} (x^{8} y^{6} + 3 x^{7} 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^{8} y^{6}) + \frac{\partial}{\partial x} (3 x^{7} y)

\frac{\partial}{\partial x} (x^{8} y^{6}) = 8 y^{6} x^{7}

\frac{\partial}{\partial x} (3 x^{7} y) = 21 y x^{6}

= 8 y^{6} x^{7} + 21 y x^{6}

\int (x^{2} x - 5) d x

x \to 0 + lim (\frac{7 x}{sin ( x )})

t an g e n t f (x) = (x^{4} - 2 x + 8)^{6}, at x = 1

\int e^{x^{2}} 2 x^{3} d x

x \to \infty lim (- 5)