derivative of (3x-5/(2x+3))

解答

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

\frac{19}{( 2 x + 3 ) ^{2}}

求解步骤

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

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

\frac{d}{d x} (3 x - 5) = 3

\frac{d}{d x} (2 x + 3) = 2

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

乘开

3 (2 x + 3) - 2 (3 x - 5) : 19

= \frac{19}{( 2 x + 3 ) ^{2}}

x \to 0 lim ((sin (\frac{x}{2}))^{x})

\int \frac{x ^{2}}{x ^{3}} d x

\int 4^{t} d t

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

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