(\partial)/(\partial y)(Ax+By^2+Cx^2y)

Lösung

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

x^{2} C + 2 B y

Schritte zur Lösung

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

Behandle

A, x, B, C

als Konstanten

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial y} (A x) + \frac{\partial}{\partial y} (B y^{2}) + \frac{\partial}{\partial y} (C x^{2} y)

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

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

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

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

Vereinfache

= x^{2} C + 2 B y

y d x + (y - x) d y = 0

s l o p e (0.3) (2.5)

\int \frac{1}{x + 5} d x

\int \frac{1}{t ^{2}} sin (\frac{2}{1} + 3) d t

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