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

Lösung

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

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

Schritte zur Lösung

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

Behandle

z, y

als Konstanten

Entferne die Konstante:

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

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

Wende die Kettenregel an:

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

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

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

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

\frac{\partial}{\partial x} (x y + z^{3} x - 2 yz)

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

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

t \to 1 lim (f (t))

y^{^{''}} + 16 y = 5 sec (4 t)