(\partial)/(\partial y)(8x-(x+y)^3)

Lösung

\frac{\partial}{\partial y} (8 x - (x + y)^{3})

- 3 x^{2} - 6 x y - 3 y^{2}

Schritte zur Lösung

\frac{\partial}{\partial y} (8 x - (x + y)^{3})

Vereinfache

8 x - (x + y)^{3} : 8 x - x^{3} - 3 x^{2} y - 3 x y^{2} - y^{3}

= \frac{\partial}{\partial y} (8 x - x^{3} - 3 x^{2} y - 3 x y^{2} - y^{3})

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial y} (8 x) - \frac{\partial}{\partial y} (x^{3}) - \frac{\partial}{\partial y} (3 x^{2} y) - \frac{\partial}{\partial y} (3 x y^{2}) - \frac{\partial}{\partial y} (y^{3})

\frac{\partial}{\partial y} (8 x) = 0

\frac{\partial}{\partial y} (x^{3}) = 0

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

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

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

= 0 - 0 - 3 x^{2} - 6 x y - 3 y^{2}

Vereinfache

= - 3 x^{2} - 6 x y - 3 y^{2}

d er i v a t i v e (\frac{2}{x} - 1)^{- 1}

x \to 0 lim (ln (\frac{x}{3}) + x^{2} - 8)

l a pl a ce t r an s f or m \frac{2}{3} t^{3} e^{- 8 t}

\frac{d}{d x} (3 cos (x) - sin (x))

\int \frac{x + 9}{16 - ( x - 4 ) ^{2}} d x