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

Lösung

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

2 x + y + 2

Schritte zur Lösung

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

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

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

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

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

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

= 2 x + y + 0 + 2 - 0

Vereinfache

= 2 x + y + 2

\frac{d}{d t} (- cos (2 t))

\int (2 x^{4} - 8 x^{3}) \cdot e^{- 3 x} d x

(2 x y) d y + (x^{2} + y^{2}) d x = 0

d er i v a t i v e y = (tan (x))^{\frac{9}{x}}

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