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Beliebt Rechnen >

(\partial)/(\partial y)(ysin(xy))

Lösung

\frac{\partial}{\partial y} (y sin (x y))

Lösung

sin (y x) + y x cos (y x)

Schritte zur Lösung

\frac{\partial}{\partial y} (y sin (x y))

Behandle

x

als Konstante

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = y, g = sin (x y)

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

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

\frac{\partial}{\partial y} (sin (x y)) = cos (x y) x

= 1 \cdot sin (x y) + cos (x y) x y

Vereinfache

= sin (y x) + y x cos (y x)

Beliebte Beispiele

derivative of (ln(x)^5)

\frac{d}{d x} ((ln (x))^{5})

integral of 8xe^{8x}

\int 8 x e^{8 x} d x

derivative ln^3(x)

d er i v a t i v e ln^{3} (x)

(dy}{dx}=\frac{(1-3y)^2)/x ,y(1)=1

\frac{d y}{d x} = \frac{( 1 - 3 y ) ^{2}}{x}, y (1) = 1

derivative of (x^2+1^2)

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