derivative (ax+b)/(cx+d)

解答

导数

\frac{a x + b}{c x + d}

\frac{- b c + a d}{( c x + d ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{a x + b}{c x + d})

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} ( a x + b ) ( c x + d ) - \frac{d}{d x} ( c x + d ) ( a x + b )}{( c x + d ) ^{2}}

\frac{d}{d x} (a x + b) = a

\frac{d}{d x} (c x + d) = c

= \frac{a ( c x + d ) - c ( a x + b )}{( c x + d ) ^{2}}

乘开

a (c x + d) - c (a x + b) : - b c + a d

= \frac{- b c + a d}{( c x + d ) ^{2}}

\frac{d}{d x} (2 x e^{2 x} + 2 x^{2} e^{2 x})

\int a sin (x) d x

\frac{d}{d x} (cos (x^{2} + y^{2}))

a re a y^{2} = 4 x, y = 2 x + 4

y^{^{''}} + 9 y = - 30 sin (3 t)