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

Lösung

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

2 x y + 3 y

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{2} y + 3 x y + 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} (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} (y^{2}) = 0

= 2 y x + 3 y + 0

Vereinfache

= 2 x y + 3 y

x \to \infty lim ((\frac{( 2 x - 3 )}{( 2 x + 5 )})^{2 x + 1})

a re a x = \frac{4}{y}, x = \frac{y}{8}, x = 8 y

\frac{\partial}{\partial x} (\frac{3 x + t}{x - 5 t})

\int_{1}^{2} (8 x^{3} + 3 x^{2}) d x

\frac{d}{d x} (\frac{x ^{3}}{3} - x)