(\partial)/(\partial x)(5(y-3)^3(x-6))

Lösung

\frac{\partial}{\partial x} (5 \cdot (y - 3)^{3} \cdot (x - 6))

5 (y - 3)^{3}

Schritte zur Lösung

\frac{\partial}{\partial x} (5 (y - 3)^{3} (x - 6))

Behandle

y

als Konstante

Entferne die Konstante:

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

= 5 (y - 3)^{3} \frac{\partial}{\partial x} (x - 6)

Wende die Summen-/Differenzregel an:

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

= 5 (y - 3)^{3} (\frac{\partial}{\partial x} (x) - \frac{\partial}{\partial x} (6))

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

\frac{\partial}{\partial x} (6) = 0

= 5 (y - 3)^{3} (1 - 0)

Vereinfache

= 5 (y - 3)^{3}

\frac{\partial}{\partial y} (x^{8 y})

\frac{\partial}{\partial s} (t^{2})

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

\frac{\partial}{\partial x} (7 - e^{x yz})

\int cos (θ) cos^{5} (sin (θ)) d θ