derivative f(x)=(2(-x^2+1))/((x^2+1))

解答

导数

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

- \frac{8 x}{( x ^{2} + 1 ) ^{2}}

求解步骤

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

将常数提出:

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

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

使用微分除法定则:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

化简

2 \cdot \frac{( - 2 x ) ( x ^{2} + 1 ) - 2 x ( - x ^{2} + 1 )}{( x ^{2} + 1 ) ^{2}} : - \frac{8 x}{( x ^{2} + 1 ) ^{2}}

= - \frac{8 x}{( x ^{2} + 1 ) ^{2}}

t an g e n t f (x) = 2 3 x, at x = 64

\frac{d}{d x} (x^{5} - 20 x^{3} + 64 x)

\frac{d}{d x} (\frac{10 x ^{3}}{x ^{2} - 1})

\int \frac{( x ^{2} - 16 )}{x} d x

\frac{d}{d x} (arctan (ln (x)))