(\partial)/(\partial x)(2/(x^2+1))

解答

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

- \frac{4 x}{( x ^{2} + 1 ) ^{2}}

求解步骤

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

将常数提出:

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

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

使用指数法则:

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

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

使用连锁律:

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

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

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

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

化简

2 (- \frac{1}{( x ^{2} + 1 ) ^{2}} \cdot 2 x) : - \frac{4 x}{( x ^{2} + 1 ) ^{2}}

= - \frac{4 x}{( x ^{2} + 1 ) ^{2}}

t an g e n t 2 x y^{3} + x y = 18, (6, 1)

l a pl a ce t r an s f or m \frac{1}{e ^{j t}}

\frac{d}{d x} (e^{x} (x - 9))

\frac{d}{d x} (\frac{x ^{5} + 5}{x ^{3}})

a re a 4 x^{2} + 10, 2 x + 7, - 3, 2