derivative of (1-5x/(1+5x))

解答

\frac{d}{d x} (\frac{1 - 5 x}{1 + 5 x})

- \frac{10}{( 1 + 5 x ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{1 - 5 x}{1 + 5 x})

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} ( 1 - 5 x ) ( 1 + 5 x ) - \frac{d}{d x} ( 1 + 5 x ) ( 1 - 5 x )}{( 1 + 5 x ) ^{2}}

\frac{d}{d x} (1 - 5 x) = - 5

\frac{d}{d x} (1 + 5 x) = 5

= \frac{( - 5 ) ( 1 + 5 x ) - 5 ( 1 - 5 x )}{( 1 + 5 x ) ^{2}}

化简

\frac{( - 5 ) ( 1 + 5 x ) - 5 ( 1 - 5 x )}{( 1 + 5 x ) ^{2}} : - \frac{10}{( 1 + 5 x ) ^{2}}

= - \frac{10}{( 1 + 5 x ) ^{2}}

\frac{\partial}{\partial y} (- 2 y e^{x^{2} - y^{2}})

\int (1 + \frac{9 x}{8}) d x

x y^{^{'}} + y = - 2 x y^{2}, y (1) = - 2

t an g e n t f (x) = x^{3} + 4 x^{2} + 5 x, at x = - 1

\int \frac{1}{4 x ^{2} + 12 x + 16} d x