erweitern (\sqrt[3]{(x+h)^2}-\sqrt[3]{x^2})/h

Lösung

erweitern

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

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

Schritte zur Lösung

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

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

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

Wende Bruchregel an:

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

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

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

e x p an d 3 cos (t) h \cdot (t - π)

e x p an d \frac{2 x + 1}{x ( x + 1 ) ( x ^{2} + 4 x + 6 )}

e x p an d - 2 u sin (t) (t - π)

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

e x p an d arctan (f (5 x^{5} - 1))