(\partial)/(\partial x)(xcos(xy))

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Produktregel an:

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

f = x, g = cos (x y)

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

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

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

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

Vereinfache

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

f (x) = x^{3} + 1

\frac{d}{d x} (arctan (x^{4} y^{3}))

\int \frac{x + 3}{x + 6} d x

x \to 0 + lim (\frac{2}{1 + ln ( x )})

\int_{- 1}^{1} (3 t - 5) d t