derivative cos((x+1)/(x-1))

Lösung

ableitung von

cos (\frac{x + 1}{x - 1})

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

Schritte zur Lösung

\frac{d}{d x} (cos (\frac{x + 1}{x - 1}))

Wende die Kettenregel an:

- sin (\frac{x + 1}{x - 1}) \frac{d}{d x} (\frac{x + 1}{x - 1})

= - sin (\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}}

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

Vereinfache

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

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

d er i v a t i v e F (x) = \frac{3}{1 + x ^{2}}

\int 3 x - 5 d x

\frac{\partial}{\partial z} (x^{2} y)

x \to π lim (+ (ln (sin (x))))

\frac{\partial}{\partial x} (\frac{x}{x ^{5} - y ^{3}})