(\partial)/(\partial y)(ycos(x-y))

Lösung

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

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

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)

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

Vereinfache

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

\frac{d}{d x} (\frac{4}{( x + 2 ) ^{2}})

\int \frac{x ^{4} + 9 x ^{2} + x + 2}{x ^{2} + 9} d x

x \to - 2 lim (\frac{2 - x}{2 + x})

n or ma l y = (x - 2)^{\frac{2}{3}}, (3, 1)

\int e^{- \frac{1}{3} x} d x