展开 (11(x+h)^2-3(x+h))/h

解答

展开

\frac{11 ( x + h ) ^{2} - 3 ( x + h )}{h}

\frac{11 x ^{2}}{h} + 22 x + 11 h - \frac{3 x}{h} - 3

求解步骤

\frac{11 ( x + h ) ^{2} - 3 ( x + h )}{h}

(x + h)^{2} = x^{2} + 2 x h + h^{2}

= \frac{11 ( x ^{2} + 2 x h + h ^{2} ) - 3 ( x + h )}{h}

乘开

11 (x^{2} + 2 x h + h^{2}) - 3 (x + h) : 11 x^{2} + 22 x h + 11 h^{2} - 3 x - 3 h

= \frac{11 x ^{2} + 22 x h + 11 h ^{2} - 3 x - 3 h}{h}

使用分式法则:

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

\frac{11 x ^{2} + 22 x h + 11 h ^{2} - 3 x - 3 h}{h} = \frac{11 x ^{2}}{h} + \frac{22 x h}{h} + \frac{11 h ^{2}}{h} - \frac{3 x}{h} - \frac{3 h}{h}

= \frac{11 x ^{2}}{h} + \frac{22 x h}{h} + \frac{11 h ^{2}}{h} - \frac{3 x}{h} - \frac{3 h}{h}

消掉

\frac{22 x h}{h} : 22 x

= \frac{11 x ^{2}}{h} + 22 x + \frac{11 h ^{2}}{h} - \frac{3 x}{h} - \frac{3 h}{h}

消掉

\frac{11 h ^{2}}{h} : 11 h

= \frac{11 x ^{2}}{h} + 22 x + 11 h - \frac{3 x}{h} - \frac{3 h}{h}

消掉

\frac{3 h}{h} : 3

= \frac{11 x ^{2}}{h} + 22 x + 11 h - \frac{3 x}{h} - 3

e x p an d 1 + csc (θ) (1 - sin (θ) = cot (θ) \cdot cos (θ))

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

\frac{d}{d x ( w )} ((w (x (w), y (w), z (w))) (x (w) y (w) + y (w) z (w) + z (w) x (w)))

e x p an d x^{8}

e x p an d \frac{19 s + 9}{( s ^{2} + 9 ) ( 2 s - 1 )}