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

Lösung

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

\frac{3 x ^{2} + 2 x ^{2} \frac{d y}{d x} - 8 x y}{2 ( x - 2 y ) x - 2 y}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

\frac{2 x x - 2 y - \frac{1 - 2 \frac{d y}{d x}}{2 x - 2 y} x ^{2}}{( x - 2 y ) ^{2}} : \frac{3 x ^{2} + 2 x ^{2} \frac{d y}{d x} - 8 x y}{2 ( x - 2 y ) x - 2 y}

= \frac{3 x ^{2} + 2 x ^{2} \frac{d y}{d x} - 8 x y}{2 ( x - 2 y ) x - 2 y}

\int \frac{3 x}{6 x ^{2} + 9} d x

\int \frac{arcsin ( x )}{1 - x} d x

\frac{d}{d x} (\frac{x ^{2}}{x + 7})

n = 1 \sum \infty sin (\frac{1}{n})

\int sec^{6} (2 x) d x