d/(d{x)}(({f}(x,y)){f}(x,y)({x}^3-3{x}{y}+{y}^2))

Lösung

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

f (x, y) f (x, y) (3 x^{2} - 3 y + 0)

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Summen-/Differenzregel an:

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

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

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

\frac{d}{d x} (3 x y) = 3 y

\frac{d}{d x} (y^{2}) = 0

= f (x, y) f (x, y) (3 x^{2} - 3 y + 0)

\frac{\partial}{\partial t} ((x) (x^{2} + y^{2}))

e x p an d \frac{K}{x ( 1 - x T )}

e x p an d (x^{2} + 1) y^{'} (x) + x y - 2 x

e x p an d (1 + \frac{1}{s}) (\frac{s}{s ^{2} + 1} + s + 1)

e x p an d 2 (ln (3) - 2 + \frac{2}{3})