(\partial)/(\partial x)(8y^6x^7-7y^5x^6)

解答

\frac{\partial}{\partial x} (8 y^{6} x^{7} - 7 y^{5} x^{6})

56 y^{6} x^{6} - 42 y^{5} x^{5}

求解步骤

\frac{\partial}{\partial x} (8 y^{6} x^{7} - 7 y^{5} x^{6})

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} (8 y^{6} x^{7}) - \frac{\partial}{\partial x} (7 y^{5} x^{6})

\frac{\partial}{\partial x} (8 y^{6} x^{7}) = 56 y^{6} x^{6}

\frac{\partial}{\partial x} (7 y^{5} x^{6}) = 42 y^{5} x^{5}

= 56 y^{6} x^{6} - 42 y^{5} x^{5}

t an g e n t y = 3 x^{2} + 4 x + 4, (1, 1)

a re a - 0.0087 x^{2} - 0.4587 x + 18.031, [0, 15]

\frac{d}{d x} (\frac{e ^{x}}{2 x ^{2} + 9})

x \cdot y \cdot y^{^{'}} = 1 - x^{2}

\frac{d}{d x} (\frac{x ^{3} - x}{x})