derivative of (cos(sqrt(x))/x)

Lösung

\frac{d}{d x} (\frac{cos ( x )}{x})

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

Schritte zur Lösung

\frac{d}{d x} (\frac{cos ( x )}{x})

Wende die Quotientenregel an:

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

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

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

\frac{d x}{d x} = 1

= \frac{( - \frac{s i n ( x )}{2 x} ) x - 1 \cdot cos ( x )}{x ^{2}}

Vereinfache

\frac{( - \frac{s i n ( x )}{2 x} ) x - 1 \cdot cos ( x )}{x ^{2}} : \frac{- x sin ( x ) - 2 cos ( x )}{2 x ^{2}}

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

(2 x y^{2} - 3) d x + (2 x^{2} y + 4) d y = 0

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

\frac{d}{d x} (\frac{( x ^{2} )}{2})

t an g e n t (3)^{x}

\frac{\partial}{\partial x} (5 y e^{x} - ln (z))