(\partial)/(\partial y)(x^3-6xy+8y^3)

Lösung

\frac{\partial}{\partial y} (x^{3} - 6 x y + 8 y^{3})

24 y^{2} - 6 x

Schritte zur Lösung

\frac{\partial}{\partial y} (x^{3} - 6 x y + 8 y^{3})

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial y} (x^{3}) - \frac{\partial}{\partial y} (6 x y) + \frac{\partial}{\partial y} (8 y^{3})

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

\frac{\partial}{\partial y} (6 x y) = 6 x

\frac{\partial}{\partial y} (8 y^{3}) = 24 y^{2}

= 0 - 6 x + 24 y^{2}

Vereinfache

= 24 y^{2} - 6 x

\frac{\partial}{\partial x} (cos (7 x + 4 y + z))

x \to 0 lim (\frac{ln ( 1 - 3 x )}{x})

\int 15 x^{2} - cos (x) + C x + C d x

d er i v a t i v e f (x) = \frac{( x ^{2} - 4 x )}{x + 1}

x \to 0 + lim (ln (\frac{7}{x ^{5}}))