(\partial)/(\partial y)(xln(x+2y+3z))

解答

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

\frac{2 x}{x + 2 y + 3 z}

求解步骤

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

将

x, z

视为常数

将常数提出:

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

= x \frac{\partial}{\partial y} (ln (x + 2 y + 3 z))

使用连锁律:

\frac{1}{x + 2 y + 3 z} \frac{\partial}{\partial y} (x + 2 y + 3 z)

= \frac{1}{x + 2 y + 3 z} \frac{\partial}{\partial y} (x + 2 y + 3 z)

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

= x \frac{1}{x + 2 y + 3 z} \cdot 2

化简

x \frac{1}{x + 2 y + 3 z} \cdot 2 : \frac{2 x}{x + 2 y + 3 z}

= \frac{2 x}{x + 2 y + 3 z}

\frac{\partial}{\partial x} (\frac{x ^{3}}{3})

x \to 0 lim (4 x^{2})

\int \frac{x}{( x ^{2} + 1 ) ^{\frac{25}{2}}} d x

\frac{d}{d x} ((2 x^{- 1})^{2})

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