(\partial)/(\partial x)(3x^3+y^3-12xy)

Lösung

\frac{\partial}{\partial x} (3 x^{3} + y^{3} - 12 x y)

9 x^{2} - 12 y

Schritte zur Lösung

\frac{\partial}{\partial x} (3 x^{3} + y^{3} - 12 x y)

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (3 x^{3}) + \frac{\partial}{\partial x} (y^{3}) - \frac{\partial}{\partial x} (12 x y)

\frac{\partial}{\partial x} (3 x^{3}) = 9 x^{2}

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

\frac{\partial}{\partial x} (12 x y) = 12 y

= 9 x^{2} + 0 - 12 y

Vereinfache

= 9 x^{2} - 12 y

x \to - 2 lim (7 x + 4)

x \to 8 - lim (\frac{5}{( x - 8 ) ^{2}})

s im pl i f y \frac{q x + r}{s x + t}

\int 4 x^{5} - 2 x^{3} + x - 2 d x

\frac{d}{d x} (\frac{x - x ^{2}}{1 + 3 x ^{2}})