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

Lösung

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

6 y^{2} - 6

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

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

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

= 6 y^{2} - 6 + 0

Vereinfache

= 6 y^{2} - 6

x \to + 0 + lim (\frac{1}{x} - \frac{1}{x ^{2} + x})

x \to 0 lim (x^{4} sin (\frac{4}{x}))

in v erse l a pl a ce \frac{1 + 4 s}{s ( 2 s ^{2} + 2 s + 1 )}

x \to 1 lim (\frac{x ^{5} - 1}{x - 1})

\frac{d}{d x} (sin (\frac{π x}{4}))