derivative of (xcos(pix+1)/(1-x))

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Vereinfache

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

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

in v erse l a pl a ce \frac{s + 1}{s ^{2} + 2}

(y - x 2) d x + (x + y 2) d y = 0

\int (\frac{- 4}{x}) d x

\int \frac{1}{n} sin (n x) d x

in v erse l a pl a ce \frac{104}{s ^{2} + 8 s + 52}