erweitern (f(x+h)-f(x^2-1))/h

Lösung

erweitern

\frac{f ( x + h ) - f ( x ^{2} - 1 )}{h}

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

Schritte zur Lösung

\frac{f ( x + h ) - f ( x ^{2} - 1 )}{h}

Multipliziere aus

f (x + h) - f (x^{2} - 1) : f x + f h - f x^{2} + f

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

Wende Bruchregel an:

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

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

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

Streiche

\frac{f h}{h} : f

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

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

e x p an d (\frac{5 x + c}{2})^{2}

e x p an d \frac{20 x ^{3}}{4 x}

e x p an d - 1 (y - x = 10)

\frac{d}{d y} ((x) (6 x + ln (6 y)))