(\partial)/(\partial x)(5y^3e^{x-2}-2xy)

解答

\frac{\partial}{\partial x} (5 y^{3} e^{x - 2} - 2 x y)

5 y^{3} e^{x - 2} - 2 y

求解步骤

\frac{\partial}{\partial x} (5 y^{3} e^{x - 2} - 2 x 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} (5 y^{3} e^{x - 2}) - \frac{\partial}{\partial x} (2 x y)

\frac{\partial}{\partial x} (5 y^{3} e^{x - 2}) = 5 y^{3} e^{x - 2}

\frac{\partial}{\partial x} (2 x y) = 2 y

= 5 y^{3} e^{x - 2} - 2 y

\int (x e^{- x^{2}} + \frac{e ^{x}}{e ^{x} + 3}) d x

\int_{- 2}^{3} \frac{15}{x ^{4}} d x

\frac{d y}{d x} = - (3 - y)^{2}

x \to \infty lim (\frac{14}{x})

d er i v a t i v e (\frac{( x - 6 )}{( x + 7 )})^{3}