(\partial)/(\partial x)(y/(2-x))

解答

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

\frac{y}{( 2 - x ) ^{2}}

求解步骤

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

将

y

视为常数

将常数提出:

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

= y \frac{\partial}{\partial x} (\frac{1}{2 - x})

使用指数法则:

\frac{1}{a} = a^{- 1}

= y \frac{\partial}{\partial x} ((2 - x)^{- 1})

使用连锁律:

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

= - \frac{1}{( 2 - x ) ^{2}} \frac{\partial}{\partial x} (2 - x)

\frac{\partial}{\partial x} (2 - x) = - 1

= y (- \frac{1}{( 2 - x ) ^{2}} (- 1))

化简

y (- \frac{1}{( 2 - x ) ^{2}} (- 1)) : \frac{y}{( 2 - x ) ^{2}}

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

d er i v a t i v e 5 \frac{1}{y ^{2}}

d er i v a t i v e f (x) = \frac{4 x - 1}{x + 5}

t an g e n t f (x) = (5 x - x^{2}) (5 - x - x^{2})

\frac{\partial}{\partial t} (t^{2} x - t)

\int \frac{x}{x ^{2} + 9} d x