(\partial)/(\partial x)(2x^6y^5+3x^5y^6)

解答

\frac{\partial}{\partial x} (2 x^{6} y^{5} + 3 x^{5} y^{6})

12 y^{5} x^{5} + 15 y^{6} x^{4}

求解步骤

\frac{\partial}{\partial x} (2 x^{6} y^{5} + 3 x^{5} y^{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} (2 x^{6} y^{5}) + \frac{\partial}{\partial x} (3 x^{5} y^{6})

\frac{\partial}{\partial x} (2 x^{6} y^{5}) = 12 y^{5} x^{5}

\frac{\partial}{\partial x} (3 x^{5} y^{6}) = 15 y^{6} x^{4}

= 12 y^{5} x^{5} + 15 y^{6} x^{4}

\int 7 x^{7} e^{- x^{4}} d x

(ln (5 x))^{^{'}}

\int_{0}^{2} \frac{x}{1 + 2 x ^{2}} d x

\frac{d}{d x} (\frac{e ^{x}}{4 x ^{2}})

\frac{d y}{d x} = (x - 1) (1 - y)