(\partial)/(\partial x)(5x^5y^4+7x^6y^8)

解答

\frac{\partial}{\partial x} (5 x^{5} y^{4} + 7 x^{6} y^{8})

25 y^{4} x^{4} + 42 y^{8} x^{5}

求解步骤

\frac{\partial}{\partial x} (5 x^{5} y^{4} + 7 x^{6} y^{8})

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} (5 x^{5} y^{4}) + \frac{\partial}{\partial x} (7 x^{6} y^{8})

\frac{\partial}{\partial x} (5 x^{5} y^{4}) = 25 y^{4} x^{4}

\frac{\partial}{\partial x} (7 x^{6} y^{8}) = 42 y^{8} x^{5}

= 25 y^{4} x^{4} + 42 y^{8} x^{5}

\frac{d}{d x} (\frac{7 x}{8})

t an g e n t f (x) = \frac{1}{9 x}, at x = 9

\int 0.1

d er i v a t i v e f (x) = 4 e^{x^{- 3}}

\frac{\partial}{\partial y} (sin (2 x + 3 y))