derivative of (y-2x/(2y-x))

解答

\frac{d}{d x} (\frac{y - 2 x}{2 y - x})

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

求解步骤

\frac{d}{d x} (\frac{y - 2 x}{2 y - 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} ( y - 2 x ) ( 2 y - x ) - \frac{d}{d x} ( 2 y - x ) ( y - 2 x )}{( 2 y - x ) ^{2}}

\frac{d}{d x} (y - 2 x) = \frac{d y}{d x} - 2

\frac{d}{d x} (2 y - x) = 2 \frac{d y}{d x} - 1

= \frac{( \frac{d y}{d x} - 2 ) ( 2 y - x ) - ( 2 \frac{d y}{d x} - 1 ) ( y - 2 x )}{( 2 y - x ) ^{2}}

乘开

(\frac{d y}{d x} - 2) (2 y - x) - (2 \frac{d y}{d x} - 1) (y - 2 x) : 3 x \frac{d y}{d x} - 3 y

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

ma c l a u r in \frac{1}{1 + 2 x}

\int \frac{x ^{3} - 1}{x} d x

\frac{d y}{d x} = 21 x^{2} e^{- y}

a re a x + y = 2, x = y^{2} - 2 y

\frac{d}{d x} (\frac{( x ^{2} - 5 ) ^{3}}{125})