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

解答

导数

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

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

求解步骤

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

使用微分除法定则:

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

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

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

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

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

化简

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

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

d er i v a t i v e f (x)

s l o p e in t erce pt (- 5, 5), (5, - 5)

(ln (3))^{^{'}}

\frac{\partial}{\partial x} (z + 1 - x e^{y} cos (z))

d er i v a t i v e y = (arctan (3 x))^{2}