(\partial)/(\partial y)(y+3xy^2-18)

Lösung

\frac{\partial}{\partial y} (y + 3 x y^{2} - 18)

6 y x + 1

Schritte zur Lösung

\frac{\partial}{\partial y} (y + 3 x y^{2} - 18)

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial y} (y) + \frac{\partial}{\partial y} (3 x y^{2}) - \frac{\partial}{\partial y} (18)

\frac{\partial}{\partial y} (y) = 1

\frac{\partial}{\partial y} (3 x y^{2}) = 6 x y

\frac{\partial}{\partial y} (18) = 0

= 1 + 6 x y - 0

Vereinfache

= 6 y x + 1

d er i v a t i v e f (s) = \frac{s}{4}

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

\int \frac{x}{x - 11} d x

d er i v a t i v e f (x) = \frac{x ^{3} - 2 x + 5}{x ^{3}}

\frac{d}{d x} (9 x^{2} + 4)