derivative of (3-x^2/(3+x^2))

解答

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

- \frac{12 x}{( 3 + x ^{2} ) ^{2}}

求解步骤

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

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

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

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

化简

\frac{( - 2 x ) ( 3 + x ^{2} ) - 2 x ( 3 - x ^{2} )}{( 3 + x ^{2} ) ^{2}} : - \frac{12 x}{( 3 + x ^{2} ) ^{2}}

= - \frac{12 x}{( 3 + x ^{2} ) ^{2}}

\frac{d y}{d x} = 6 y e^{x + 9}

x \to 0 lim ((1 - \frac{1}{x})^{x})

x \to 1 lim (\frac{0}{x - 1})

d er i v a t i v e (4 x + 3)^{4} (x + 1)^{- 3}

\frac{\partial}{\partial v} (\frac{v}{u - v})