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Beliebt Rechnen >

derivative of (x^2-1/(x^2+1))

Lösung

\frac{d}{d 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 2t-4

\int 2 t - 4 d t

laplacetransform f(t)=2e^{-t}cos(4t)1(t)

l a pl a ce t r an s f or m f (t) = 2 e^{- t} cos (4 t) 1 (t)

(dy)/(dx)=(2sqrt(y+1)cos(x))

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

integral of-6/(x^4)

\int - \frac{6}{x ^{4}} d x

integral from 0 to 1 of (x^2+y^2+z^2)

\int_{0}^{1} (x^{2} + y^{2} + z^{2}) d x