(\partial)/(\partial y)(xzcos(x+yz))

Lösung

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

- x z^{2} sin (x + zy)

Schritte zur Lösung

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

Behandle

x, z

als Konstanten

Entferne die Konstante:

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

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

Wende die Kettenregel an:

- sin (x + yz) \frac{\partial}{\partial y} (x + yz)

= - sin (x + yz) \frac{\partial}{\partial y} (x + yz)

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

= x z (- sin (x + yz) z)

Vereinfache

x z (- sin (x + yz) z) : - x z^{2} sin (x + zy)

= - x z^{2} sin (x + zy)

\frac{d}{d x} (sin^{2} (ln (x)))

d er i v a t i v e \frac{3 x}{9 x ^{2} + 4 x - 9}

\int_{0}^{1} \frac{1}{4 x} d x

x \to 1 lim (\frac{[ x ]}{∣ x ∣})

x \to π lim (sin (6 x))