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

Lösung

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

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

Schritte zur Lösung

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

Vereinfache

\frac{- x ^{2}}{y ^{2}} : - \frac{x ^{2}}{y ^{2}}

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Quotientenregel an:

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

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

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

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

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

Streiche

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

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

d er i v a t i v e f (x) = \frac{x ^{2}}{2} \cdot cos^{3} (\frac{1}{x})

n = 2 \sum \infty 3 (\frac{x}{4})^{n}

\int x^{2} \cdot e^{x} d x

\int (2 t + 4) d t

y^{^{'}} = x (1 - y^{2})