(\partial)/(\partial x)(4x^3y^3-18y-x)

Lösung

\frac{\partial}{\partial x} (4 x^{3} y^{3} - 18 y - x)

12 x^{2} y^{3} - 1

Schritte zur Lösung

\frac{\partial}{\partial x} (4 x^{3} y^{3} - 18 y - x)

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (4 x^{3} y^{3}) - \frac{\partial}{\partial x} (18 y) - \frac{\partial}{\partial x} (x)

\frac{\partial}{\partial x} (4 x^{3} y^{3}) = 12 y^{3} x^{2}

\frac{\partial}{\partial x} (18 y) = 0

\frac{\partial}{\partial x} (x) = 1

= 12 y^{3} x^{2} - 0 - 1

Vereinfache

= 12 x^{2} y^{3} - 1

\frac{\partial}{\partial y} (9 x sin (y - z))

\int_{- 4}^{- 1} x^{4} d x

\frac{d y}{d x} = 2 y (1 - \frac{y}{4})

\frac{d}{d x} (x^{3} arccos (x))

\frac{d}{d x} (\frac{1}{4} x^{4} - x^{3})