derivative of x/(5x+8)

解答

\frac{d}{d x} (\frac{x}{5 x + 8})

\frac{8}{( 5 x + 8 ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{x}{5 x + 8})

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} ( 5 x + 8 ) - \frac{d}{d x} ( 5 x + 8 ) x}{( 5 x + 8 ) ^{2}}

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

\frac{d}{d x} (5 x + 8) = 5

= \frac{1 \cdot ( 5 x + 8 ) - 5 x}{( 5 x + 8 ) ^{2}}

化简

= \frac{8}{( 5 x + 8 ) ^{2}}

x \to - 2 + lim (\frac{1 - x}{x + 2})

\frac{\partial}{\partial x} (x^{5})

\int cos (4 x) sin^{5} (4 x) d x

d er i v a t i v e f (x) = \frac{x ^{2}}{x - 1}

t an g e n t 4 (8 x - 1)^{4}