(\partial)/(\partial y)(x^2sin^2(yz))

Lösung

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

x^{2} z sin (2 yz)

Schritte zur Lösung

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

Behandle

x, z

als Konstanten

Entferne die Konstante:

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

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

Wende die Kettenregel an:

2 sin (yz) \frac{\partial}{\partial y} (sin (yz))

= 2 sin (yz) \frac{\partial}{\partial y} (sin (yz))

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

= x^{2} \cdot 2 sin (yz) cos (yz) z

Verwende die Doppelwinkelidentität:

2 sin (x) cos (x) = sin (2 x)

= x^{2} z sin (2 yz)

\int x^{n - 1} d x

in v erse l a pl a ce \frac{1}{s}

\int sec^{2} (θ) + 6 d θ

d er i v a t i v e \frac{x ^{2}}{1 + x}

\frac{d}{d r} (ln (r))