derivative x/(x-4)

解答

导数

\frac{x}{x - 4}

- \frac{4}{( x - 4 ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{x}{x - 4})

使用微分除法定则:

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

= \frac{\frac{d x}{d x} ( x - 4 ) - \frac{d}{d x} ( x - 4 ) x}{( x - 4 ) ^{2}}

\frac{d x}{d x} = 1

\frac{d}{d x} (x - 4) = 1

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

化简

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

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

d er i v a t i v e \frac{- 2 x ^{2} + 9}{9 - x ^{2}}

\int_{7}^{8} (\frac{1}{x ^{2}} - 1) d x

(\frac{ln ( x )}{x ^{2}})^{^{'}}

\frac{\partial}{\partial x} (cos^{7} (x^{9} y^{5}))

d er i v a t i v e y = \frac{4 - x e ^{x}}{x + e ^{x}}