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

Lösung

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

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Produktregel an:

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

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

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

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

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

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

\int \frac{9 x}{( 2 - x ^{2} ) ^{3}} d x

a re a y = 3 x, y = 3, x = 0

\frac{d}{d x} (arccsc (e^{x}))

a re a 7 cos (8 x), 7 - 7 cos (8 x), [0, \frac{π}{8}]

t a y l or φ^{5} cos (φ^{2})