(\partial)/(\partial x)(12x^2y^5+x^2y^2)

Lösung

\frac{\partial}{\partial x} (12 x^{2} y^{5} + x^{2} y^{2})

24 y^{5} x + 2 y^{2} x

Schritte zur Lösung

\frac{\partial}{\partial x} (12 x^{2} y^{5} + x^{2} y^{2})

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (12 x^{2} y^{5}) + \frac{\partial}{\partial x} (x^{2} y^{2})

\frac{\partial}{\partial x} (12 x^{2} y^{5}) = 24 y^{5} x

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

= 24 y^{5} x + 2 y^{2} x

x \to 0 lim (x^{4} f (x))

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

2 y (x + 1) d y = x d x

t a y l or \frac{1}{x ^{2}}, at 4

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