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}})

Entferne die Konstante:

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

= - \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}}

Streiche

\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}}

\frac{\partial}{\partial x} (x^{5} + x y^{7} + 6)

\frac{d}{d x} (3 9 x^{2} + 7)

t an g e n t f (x) = 4 cos (x), (\frac{π}{3}, 2)

\frac{\partial}{\partial w} (t e^{\frac{w}{t}})

\int \frac{x e ^{3 x}}{2} d x