derivative of ((2pi-xcos(x))/(x-2pi))

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

\frac{d}{d x} (x - 2 π) = 1

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

Vereinfache

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

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

e x p an d \frac{( 3 x ^{2} - 4 ) ( x ^{2} - 6 )}{x ^{2} + 4}

\frac{\partial}{\partial y} (\frac{x}{y + x})

\frac{d}{d x} ((x^{2} + 3)^{s i n (x)})

l a pl a ce t r an s f or m e^{3 t} (9 - 4 t + 10 sin (\frac{t}{2}))

x \to 0 + lim (x ln (e^{x} - 1))