(\partial)/(\partial y)(xy^2-6x^2-3y^2)

Lösung

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

2 x y - 6 y

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

\frac{\partial}{\partial y} (6 x^{2}) = 0

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

= 2 x y - 0 - 6 y

Vereinfache

= 2 x y - 6 y

d er i v a t i v e y = (8 x^{3} + 5)^{\frac{3}{2}}

a re a y = e^{x}, y = e^{- 2 x}, x = ln (6)

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

d er i v a t i v e \frac{480 x}{( x ^{2} + 5 ) ^{3}}

\frac{d}{d x} (ln (x^{2} - 5))