(\partial)/(\partial x)((z)(x^2+xy^2z))

Lösung

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

z (2 x + z y^{2})

Schritte zur Lösung

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

Behandle

z, y

als Konstanten

Entferne die Konstante:

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

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

Wende die Summen-/Differenzregel an:

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

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

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

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

= z (2 x + z y^{2})

\frac{d}{d y} ((x) ((1 + 2 x)^{6}))

s im pl i f y 3 (1 - 2 sin^{2} (x) cos^{2} (x))

e x p an d a (- 3, - 2) b (5, 3)

s im pl i f y (x + 15 + x)^{2}

s im pl i f y 2 (2 x cos^{3} (x) - 3 x^{2} cos^{2} (x) sin (x))