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Beliebt Rechnen >

derivative f(x)=((x^2-1))/(x^2+1)

Lösung

ableitung von

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

Lösung

\frac{4 x}{( x ^{2} + 1 ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( x ^{2} - 1 ) ( x ^{2} + 1 ) - \frac{d}{d x} ( x ^{2} + 1 ) ( x ^{2} - 1 )}{( x ^{2} + 1 ) ^{2}}

\frac{d}{d x} (x^{2} - 1) = 2 x

\frac{d}{d x} (x^{2} + 1) = 2 x

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

Multipliziere aus

2 x (x^{2} + 1) - 2 x (x^{2} - 1) : 4 x

= \frac{4 x}{( x ^{2} + 1 ) ^{2}}

Graph

Beliebte Beispiele

integral of 5x^2+(2/x)^4

\int 5 x^{2} + (\frac{2}{x})^{4} d x

(d^2y)/(dx^2)+y=0

\frac{d ^{2} y}{d x ^{2}} + y = 0

y^'-1/x y=x^2e^x

y^{^{'}} - \frac{1}{x} y = x^{2} e^{x}

derivative of (cos(2x)/(sin(3x)))

\frac{d}{d x} (\frac{cos ( 2 x )}{sin ( 3 x )})

integral from 0 to 16 of sqrt(t^2+2t+1)

\int_{0}^{16} t^{2} + 2 t + 1 d t