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

Lösung

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

12 y x + 6 y^{3}

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

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

\frac{\partial}{\partial x} (6 x^{2} y) = 12 y x

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

= 12 y x + 6 y^{3}

x \to - 5 lim (g (x))

\frac{d}{d x} (\frac{x}{x ^{2} + y ^{2} + z ^{2}})

in v erse l a pl a ce \frac{s + 1}{( s ^{2} - 2 s + 5 )}

\frac{\partial}{\partial x} (x yz + x y^{5} + y z^{5} + z x^{5})

a re a y = x^{2} - 3, y = 1