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

Lösung

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

\frac{4 ( x - 1 )}{( x + 1 ) ^{3}}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

= \frac{4 ( x - 1 )}{( x + 1 ) ^{3}}

\frac{d}{d x} ((6 x - 1) (3 x - 5)^{- 1})

t an g e n t f (x) = cos (\frac{π x}{2}), at x = 0.7

x y d x - (x^{2} - x) d y = 0

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

\int (x^{3} - 3)^{2} d x