(\partial)/(\partial x)(x^2y-3xy+xy^2)

Lösung

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

2 y x - 3 y + y^{2}

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

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

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

= 2 y x - 3 y + y^{2}

\int ln^{2} (x^{2}) d x

\int (2 - \frac{1}{x}) ln (x) d x

\frac{d}{d x} (10 sin (x) + 103 cos (x))

\int \frac{x ^{5} - x ^{4} + 4 x ^{2} - x}{x ^{3} + 1} d x

x \to 0 lim (x cos (\frac{7}{x}))