derivative of (-2x^2/(5y^2))

Lösung

\frac{d}{d x} (\frac{- 2 x ^{2}}{5 y ^{2}})

- \frac{4 x ( - x \frac{d y}{d x} + y )}{5 y ^{3}}

Schritte zur Lösung

\frac{d}{d x} (\frac{- 2 x ^{2}}{5 y ^{2}})

Vereinfache

\frac{- 2 x ^{2}}{5 y ^{2}} : - \frac{2 x ^{2}}{5 y ^{2}}

= \frac{d}{d x} (- \frac{2 x ^{2}}{5 y ^{2}})

Entferne die Konstante:

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

= - \frac{2}{5} \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{2}{5} \cdot \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}{5} \cdot \frac{2 x y ^{2} - 2 y \frac{d y}{d x} x ^{2}}{( y ^{2} ) ^{2}}

Vereinfache

- \frac{2}{5} \cdot \frac{2 x y ^{2} - 2 y \frac{d y}{d x} x ^{2}}{( y ^{2} ) ^{2}} : - \frac{4 x ( - x \frac{d y}{d x} + y )}{5 y ^{3}}

= - \frac{4 x ( - x \frac{d y}{d x} + y )}{5 y ^{3}}

\int_{0}^{3} \frac{2}{3 - x} d x

\frac{d}{d x} (\frac{2 x - 1}{x + 5})

\int 12 sin (x) cos (x) d x

\int \frac{3}{x ^{2} + 3 x - 10} d x

\frac{d y}{d x} + y = e^{2 x}