展开 (x(x+1)dy)/(dx)

解答

展开

\frac{x ( x + 1 ) d y}{d x}

\frac{x ^{2} d y}{d x} + \frac{x d y}{d x}

求解步骤

\frac{x ( x + 1 ) d y}{d x}

乘开

x (x + 1) d y : x^{2} d y + x d y

= \frac{x ^{2} d y + x d y}{d x}

使用分式法则:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{x ^{2} d y + x d y}{d x} = \frac{x ^{2} d y}{d x} + \frac{x d y}{d x}

= \frac{x ^{2} d y}{d x} + \frac{x d y}{d x}

e x p an d \frac{( - \frac{10}{5} x ^{4} y ^{3} z ^{2} )}{( \frac{1}{2} y ^{3} )}

e x p an d (\frac{- 21}{34} - \frac{16 x}{- 17})^{2}

e x p an d (x^{2} + x + 1) (- 15 x^{2} + 15 x - \frac{3}{2})

s im pl i f y 11 z (- z + 11)

e x p an d (- \frac{2}{9} x - \frac{1}{3}) (2 x - 3)