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

Lösung

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

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

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

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

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

\int cos (2 a x) d x

\frac{d}{d x} ((5 x^{2} + e)^{6})

n = 3 \sum \infty x^{n}

\frac{d}{d x} (\frac{6}{x} + \frac{x}{6})

\int 10 csc^{2} (x) d x