derivative of x/(sqrt(y))

Lösung

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

\frac{2 y - x \frac{d y}{d x}}{2 y y}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

= \frac{2 y - x \frac{d y}{d x}}{2 y y}

\int \frac{4}{x ( x + 6 )} d x

y^{^{'}} = \frac{x ^{2} + y ^{2}}{x y}, y (1) = 1

n = 1 \sum \infty 8 (\frac{3}{4})^{n}

\frac{\partial}{\partial x} (4 x^{2} y^{2})

s l o p e (- 2, 1), (3, - 9)