(\partial)/(\partial y)(xcos(x+y))

Lösung

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

- x sin (x + y)

Schritte zur Lösung

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

Behandle

x

als Konstante

Entferne die Konstante:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

= - x sin (x + y)

\frac{d y}{d x} + 2 y = 20 e^{3 x}

\frac{\partial}{\partial y} (\frac{7 y}{x ^{4}})

x \to 1 lim (2 x - 5)

\frac{d}{d x} (\frac{1}{8} x^{2})

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