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

Lösung

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

2 x y^{2} + y

Schritte zur Lösung

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

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

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

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

= 2 y^{2} x + y + 0

Vereinfache

= 2 x y^{2} + y

\frac{d}{d x} (6 x^{\frac{3}{2}} + 1)

\int cos^{2} (3 x) d x

f (x) = arcsin (2 x + 1)

\frac{d}{d x} (x^{2} - 2 x + 2 (x + 1))

\frac{d}{d x} (\frac{x - 1}{x - 1})