(\partial)/(\partial x)((a-b^2)/(x-c^2))

解答

\frac{\partial}{\partial x} (\frac{a - b ^{2}}{x - c ^{2}})

- \frac{a - b ^{2}}{( x - c ^{2} ) ^{2}}

求解步骤

\frac{\partial}{\partial x} (\frac{a - b ^{2}}{x - c ^{2}})

将

a, b, c

视为常数

将常数提出:

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

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

使用指数法则:

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

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

使用连锁律:

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

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

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

= (a - b^{2}) (- \frac{1}{( x - c ^{2} ) ^{2}} \cdot 1)

化简

(a - b^{2}) (- \frac{1}{( x - c ^{2} ) ^{2}} \cdot 1) : - \frac{a - b ^{2}}{( x - c ^{2} ) ^{2}}

= - \frac{a - b ^{2}}{( x - c ^{2} ) ^{2}}

\frac{d}{d x} (5 - \frac{4}{x})

d er i v a t i v e \frac{- u ^{2} + 7}{( u ^{2} + 7 ) ^{2}}

\frac{d}{d x} (sec (x^{5} + x))

s l o p e in t erce pt (1.1) (0.5)

\int 1 + 5 x^{2} (10 x) d x