derivative of (x+3/x /(sqrt(x)))

Lösung

\frac{d}{d x} (\frac{x + \frac{3}{x}}{x})

\frac{x ^{2} - 9}{2 x ^{2} x}

Schritte zur Lösung

\frac{d}{d x} (\frac{x + \frac{3}{x}}{x})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x + \frac{3}{x} ) x - \frac{d}{d x} ( x ) ( x + \frac{3}{x} )}{( x ) ^{2}}

\frac{d}{d x} (x + \frac{3}{x}) = 1 - \frac{3}{x ^{2}}

\frac{d}{d x} (x) = \frac{1}{2 x}

= \frac{( 1 - \frac{3}{x ^{2}} ) x - \frac{1}{2 x} ( x + \frac{3}{x} )}{( x ) ^{2}}

Vereinfache

\frac{( 1 - \frac{3}{x ^{2}} ) x - \frac{1}{2 x} ( x + \frac{3}{x} )}{( x ) ^{2}} : \frac{x ^{2} - 9}{2 x ^{2} x}

= \frac{x ^{2} - 9}{2 x ^{2} x}

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

\frac{d}{d x} (cot (9) (1 - 2 x^{2}))

\int ln (x^{2} - 4) d x

d er i v a t i v e \frac{1}{9 x ^{\frac{8}{9}}}

\frac{d}{d x} (\frac{1}{2} cos^{2} (5 x))