(\partial)/(\partial y)(xcos(x+2y))

Lösung

\frac{\partial}{\partial y} (x cos (x + 2 y))

- 2 x sin (x + 2 y)

Schritte zur Lösung

\frac{\partial}{\partial y} (x cos (x + 2 y))

Behandle

x

als Konstante

Entferne die Konstante:

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

= x \frac{\partial}{\partial y} (cos (x + 2 y))

Wende die Kettenregel an:

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

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

\frac{\partial}{\partial y} (x + 2 y) = 2

= x (- sin (x + 2 y) \cdot 2)

Vereinfache

= - 2 x sin (x + 2 y)

t an g e n t f (x) = \frac{1}{x + 1}, at x = 4

\int \frac{1}{( x ^{2} - 4 )} d x

\frac{d}{d x} ((x^{5} - 4 x^{3} - 7)^{8})

\frac{d}{d x} (\frac{0.07 e ^{x}}{sin ( x )})

\frac{d x}{d t} = x^{2} - x