derivative y=(sqrt(x))/x

Lösung

ableitung von

y = \frac{x}{x}

- \frac{1}{2 x ^{\frac{3}{2}}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

= \frac{\frac{1}{2 x} x - 1 \cdot x}{x ^{2}}

Vereinfache

\frac{\frac{1}{2 x} x - 1 \cdot x}{x ^{2}} : - \frac{1}{2 x ^{\frac{3}{2}}}

= - \frac{1}{2 x ^{\frac{3}{2}}}

t^{2} y^{^{''}} + 17 t y^{^{'}} + 64 y = 0

x \to 0 lim (x (0))

\frac{\partial}{\partial y} (sin (- 2 x) cos (6 y))

\frac{d}{d x} (tan (e^{π}))

\frac{d}{d x} (\frac{1}{2 x + 6})