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

Lösung

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

4 (y + 3)^{3}

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Summen-/Differenzregel an:

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

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

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

\frac{\partial}{\partial x} (4) = 0

= 4 (y + 3)^{3} (1 - 0)

Vereinfache

= 4 (y + 3)^{3}

x \to - 8 lim (∣ x ∣)

\frac{d y}{d x} = (sin (5 x))

\frac{\partial}{\partial x} (\frac{z}{y x})

x \to 0 lim (x^{t a n (x)})

d er i v a t i v e f (z) = \frac{z - 4}{z + 4}