derivative of (sqrt(x)x/(x^2))

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (x x) = \frac{3 x}{2}

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

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

Vereinfache

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

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

y^{^{'}} + 3 y = e^{- 4 t}, y (0) = 5

\frac{d}{d x} (\frac{9}{e ^{x} - e ^{- x}})

x^{2} + 3 y \frac{d y}{d x} = 0

\int_{0}^{16} \frac{1}{x} d x

y^{^{'}} = ry