(\partial)/(\partial y)(ycos(xy))

Lösung

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

cos (y x) - y x sin (y x)

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Produktregel an:

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

f = y, g = cos (x y)

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

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

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

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

Vereinfache

= cos (y x) - y x sin (y x)

\int \frac{e ^{x}}{5 - e ^{2 x}} d x

x \to \infty lim (- \frac{3}{2} x)

n = 1 \sum \infty \frac{9 ^{n}}{n !}

x \to \infty lim (3 x + x^{2})

s l o p e (0, 3), (3, 0)