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

Lösung

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

2 x - 2 x y

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

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

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

= 2 x + 0 - 2 y x

Vereinfache

= 2 x - 2 x y

\int \frac{10}{1 - x ^{2}} d x

x y^{^{''}} - 2 y^{^{'}} = 0

\int \frac{6}{( 9 t ^{2} + 1 ) ^{2}} d t

\frac{d}{d x} (A x^{2} e^{x})

\int_{0}^{3} 450.268 e^{1.12567 t} d t