(\partial)/(\partial y)(y^2sin(xy))

Lösung

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

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Produktregel an:

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

f = y^{2}, g = sin (x y)

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

\frac{\partial}{\partial y} (y^{2}) = 2 y

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

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

x \to 5 lim (\frac{2}{( x - 5 ) ^{6}})

x \to 1 lim (2 x^{- 1})

l a pl a ce t r an s f or m t e^{- 5 t} sin (5 t)

\int 6 e^{7} d x

\frac{d}{d x} (e^{2 x} + 3)