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

Lösung

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

3 x^{2} + 2 y

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

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

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

= 3 x^{2} + 2 y + 0

Vereinfache

= 3 x^{2} + 2 y

\frac{d}{d x} (0.015 + x)

t an g e n t f (x) = 6 x^{2} - 10 x + 4, at x = 1

x \to 3 lim (ln (x))

\int e^{2 y} - y cos (x y) d x

\frac{d}{d x} (4.9 x^{2})