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

Lösung

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

sin (y) + y cos (y)

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = y, g = sin (y)

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

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

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

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

Vereinfache

= sin (y) + y cos (y)

d er i v a t i v e y = 8 x sin (x^{2})

\frac{\partial}{\partial y} (7 e^{7 e^{y x} + y} x)

\frac{d}{d x} (- 4 sin (2 x) + 3 cos (3 x))

\int_{0}^{1} 6 e^{- 4 x} d x

\frac{d y}{d x} + \frac{2 x y}{1 + x ^{2}} = - 2 x y^{2}