derivative of 2/((x^2+x+1^2))

解答

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

- \frac{4 ( 2 x + 1 )}{( x ^{2} + x + 1 ) ^{3}}

求解步骤

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

将常数提出:

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

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

使用指数法则:

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

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

使用连锁律:

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

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

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

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

化简

2 (- \frac{2}{( x ^{2} + x + 1 ) ^{3}} (2 x + 1)) : - \frac{4 ( 2 x + 1 )}{( x ^{2} + x + 1 ) ^{3}}

= - \frac{4 ( 2 x + 1 )}{( x ^{2} + x + 1 ) ^{3}}

\frac{\partial}{\partial y} (2 y + 1)

d er i v a t i v e (t + 1)^{3} t^{2} + 84

d er i v a t i v e x^{2} arctan (2 x)

t a y l or e^{x - 1}, 1

d er i v a t i v e f (x) = \frac{4 x ^{2}}{( x ^{2} + x ) ^{3}}