erweitern ((x+h)^2-x)/h

Lösung

erweitern

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

\frac{x ^{2}}{h} + 2 x + h - \frac{x}{h}

Schritte zur Lösung

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

Multipliziere aus

(x + h)^{2} - x : x^{2} + 2 x h + h^{2} - x

= \frac{x ^{2} + 2 x h + h ^{2} - x}{h}

Wende Bruchregel an:

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

\frac{x ^{2} + 2 x h + h ^{2} - x}{h} = \frac{x ^{2}}{h} + \frac{2 x h}{h} + \frac{h ^{2}}{h} - \frac{x}{h}

= \frac{x ^{2}}{h} + \frac{2 x h}{h} + \frac{h ^{2}}{h} - \frac{x}{h}

Streiche

\frac{2 x h}{h} : 2 x

= \frac{x ^{2}}{h} + 2 x + \frac{h ^{2}}{h} - \frac{x}{h}

Streiche

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

= \frac{x ^{2}}{h} + 2 x + h - \frac{x}{h}

e x p an d y (x y + y + 1) d x + (2 x y + 1) d y

e x p an d \frac{x ^{2} - a}{( x - 4 ) ( x + 5 )}

e x p an d \frac{x ( x + 1 )}{t}

e x p an d \frac{5}{x ( x ^{2} - 16 )}

e x p an d e^{(t - 1)^{2}}