derivative of y/(x^2)

Lösung

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

\frac{x \frac{d y}{d x} - 2 y}{x ^{3}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

Vereinfache

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

= \frac{x \frac{d y}{d x} - 2 y}{x ^{3}}

a re a y = x^{2} - 4, y = 0

y^{^{''}} - 6 y^{^{'}} - 8 y = 0

d er i v a t i v e x + \frac{1}{x}

\frac{\partial}{\partial x} (5 x^{4} + 2 x y^{2} + 1)

\frac{d}{d y} ((\frac{1}{y ^{2}} - \frac{5}{y ^{4}}) (y + 7 y^{3}))