derivative of (x*cos(x+pi)/(pi-x))

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

\frac{d}{d x} (π - x) = - 1

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

Vereinfache

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

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

d er i v a t i v e \frac{t}{3}

\int r^{3} 1 + 4 r^{2} d r

d er i v a t i v e \frac{1}{3 ( 1 + e ^{- t} ) ^{3}}

x d y + 3 y d x = x y d y

d er i v a t i v e y = 3 t + 6 t^{3}