derivative of x-x^2y-y+xy^2

Lösung

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

1 - 2 x y - x^{2} \frac{d y}{d x} - \frac{d y}{d x} + y^{2} + 2 x y \frac{d y}{d x}

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d x}{d x} = 1

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

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

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

Vereinfache

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

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

l a pl a ce t r an s f or m e^{-} cos (t)

d er i v a t i v e e^{x 9 x + 10}

\int e^{c o s (x)} sin (x) d x

\frac{\partial}{\partial x} (- 2 sin (x))

y^{^{''}} - 2 y^{^{'}} - 3 y = 0, y (0) = 2, y^{^{'}} (0) = 2