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

Lösung

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

\frac{8 x ( x ^{2} - 1 )}{( x ^{2} + 1 ) ^{3}}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

2 \cdot \frac{x ^{2} - 1}{x ^{2} + 1} \cdot \frac{4 x}{( x ^{2} + 1 ) ^{2}} : \frac{8 x ( x ^{2} - 1 )}{( x ^{2} + 1 ) ^{3}}

= \frac{8 x ( x ^{2} - 1 )}{( x ^{2} + 1 ) ^{3}}

\frac{d}{d x} (x^{\frac{y}{z}})

\int 7 x e^{- x (y + 7)} d x

d er i v a t i v e f (x) = ln (x x^{2} + 1)

f (x) = 3 x - 6 x

\int_{1}^{x} \frac{1}{x} d x