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

Lösung

ableitung von

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

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

Schritte zur Lösung

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

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

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

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

Multipliziere aus

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

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

d er i v a t i v e f (x) = \frac{4}{3 x}

\frac{\partial}{\partial x} (\frac{( x + y )}{( x - y ) ^{2}})

h \to 0 lim (3 h + 18)

t an g e n t f (x) = \frac{1}{2} x ln (x^{2}), (- 1, 0)

\int cos (θ) + sin (θ) d θ