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

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = cos (y - x)

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

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

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

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

Vereinfache

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

\int_{- 3}^{0} \frac{1}{9 - x ^{2}} d x

\int_{0}^{20} cos (π x) d x

x \to 0 lim (\frac{x ^{2}}{x})

\frac{d}{d x} (x^{2} sin (π x))

\frac{d y}{d x} = y sec^{2} (x)