derivative of (1+sqrt(x)/x)

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

y^{^{''}} + 2 y^{^{'}} - 3 y = 0, y (0) = 4, y^{^{'}} (0) = 1

d er i v a t i v e f (x) = \frac{9}{x - 6}

x \to 0 lim (\frac{x}{sin ( 6 x )})

d er i v a t i v e f (x) = sin^{2} (e^{s i n^{2} (x)})

\frac{\partial}{\partial x} (3 y^{6} sin (3 x))