(\partial)/(\partial y)(xln(5x+8y))

解答

\frac{\partial}{\partial y} (x ln (5 x + 8 y))

\frac{8 x}{5 x + 8 y}

求解步骤

\frac{\partial}{\partial y} (x ln (5 x + 8 y))

将

x

视为常数

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= x \frac{\partial}{\partial y} (ln (5 x + 8 y))

使用连锁律:

\frac{1}{5 x + 8 y} \frac{\partial}{\partial y} (5 x + 8 y)

= \frac{1}{5 x + 8 y} \frac{\partial}{\partial y} (5 x + 8 y)

\frac{\partial}{\partial y} (5 x + 8 y) = 8

= x \frac{1}{5 x + 8 y} \cdot 8

化简

x \frac{1}{5 x + 8 y} \cdot 8 : \frac{8 x}{5 x + 8 y}

= \frac{8 x}{5 x + 8 y}

\frac{d}{d t} (0. 9^{t})

x \to 0 lim (\frac{x - 9}{x - 1})

\frac{d y}{d t} = \frac{1}{y}

\frac{d}{d x} (\frac{1}{2 x} + \frac{1}{3 x ^{\frac{2}{3}}})

(\frac{2 sin ( x )}{1 - 2 cos ( x )})^{^{'}}