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

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{\partial}{\partial x} (y) = 0

= cos (x + y) - x sin (x + y) + 0

Vereinfache

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

\int_{- 2}^{0} (x - 2) (x + 1) d x

a re a y = 8 x, y = \frac{5}{2} x, y = 9 - x^{2}

x \to 4 - lim (4 - x)

\frac{d y}{d x} = \frac{4}{x e ^{y}}

\int_{1}^{3} 11 r^{3} \cdot ln (r) d r