d/(dy)(ycos(xy))

Lösung

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

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

Schritte zur Lösung

\frac{d}{d 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{d y}{d y} cos (x y) + \frac{d}{d y} (cos (x y)) y

\frac{d y}{d y} = 1

\frac{d}{d 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)

n = 1 \sum \infty 5 \cdot 3^{n}

\frac{\partial}{\partial y} (- 2 sin (y) + x y^{3})

\int \frac{1}{( 225 + x ^{2} ) ^{\frac{3}{2}}} d x

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

\frac{d}{d x} (ln (8 x + 7))