d/(dt)((1-3t^2)/(1-2t))

解答

\frac{d}{d t} (\frac{1 - 3 t ^{2}}{1 - 2 t})

\frac{6 t ^{2} - 6 t + 2}{( 1 - 2 t ) ^{2}}

求解步骤

\frac{d}{d t} (\frac{1 - 3 t ^{2}}{1 - 2 t})

使用微分除法定则:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d t} ( 1 - 3 t ^{2} ) ( 1 - 2 t ) - \frac{d}{d t} ( 1 - 2 t ) ( 1 - 3 t ^{2} )}{( 1 - 2 t ) ^{2}}

\frac{d}{d t} (1 - 3 t^{2}) = - 6 t

\frac{d}{d t} (1 - 2 t) = - 2

= \frac{( - 6 t ) ( 1 - 2 t ) - ( - 2 ) ( 1 - 3 t ^{2} )}{( 1 - 2 t ) ^{2}}

化简

\frac{( - 6 t ) ( 1 - 2 t ) - ( - 2 ) ( 1 - 3 t ^{2} )}{( 1 - 2 t ) ^{2}} : \frac{6 t ^{2} - 6 t + 2}{( 1 - 2 t ) ^{2}}

= \frac{6 t ^{2} - 6 t + 2}{( 1 - 2 t ) ^{2}}

\frac{d}{d x} (\frac{- π x ^{2} - 4 x ^{2} + 64 x}{8})

\int \frac{4}{x ^{5}} - 5 x^{4} d x

\frac{\partial}{\partial y} (ln (x^{6} y))

n = 0 \sum \infty (\frac{2}{3})^{n}

\frac{d}{d x} (x ln^{3} (x))