derivative of (3+8x/(5-4x))

解答

\frac{d}{d x} (\frac{3 + 8 x}{5 - 4 x})

\frac{52}{( 5 - 4 x ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{3 + 8 x}{5 - 4 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} ( 3 + 8 x ) ( 5 - 4 x ) - \frac{d}{d x} ( 5 - 4 x ) ( 3 + 8 x )}{( 5 - 4 x ) ^{2}}

\frac{d}{d x} (3 + 8 x) = 8

\frac{d}{d x} (5 - 4 x) = - 4

= \frac{8 ( 5 - 4 x ) - ( - 4 ) ( 3 + 8 x )}{( 5 - 4 x ) ^{2}}

化简

\frac{8 ( 5 - 4 x ) - ( - 4 ) ( 3 + 8 x )}{( 5 - 4 x ) ^{2}} : \frac{52}{( 5 - 4 x ) ^{2}}

= \frac{52}{( 5 - 4 x ) ^{2}}

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

\frac{\partial}{\partial y} (x cos (y) sin (z))

2 y^{^{'}} + 10 y = 80, y (0) = 0

\frac{\partial}{\partial x} (8 - 2 x^{2} - y^{2})

d er i v a t i v e g (0) = (4 - 2 x) e^{n} - 4