(\partial)/(\partial x)(xycos(3x)+e^{xy})

Lösung

\frac{\partial}{\partial x} (x \cdot y \cdot cos (3 x) + e^{x y})

y (cos (3 x) - 3 x sin (3 x)) + e^{x y} y

Schritte zur Lösung

\frac{\partial}{\partial x} (x y cos (3 x) + e^{x y})

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (x y cos (3 x)) + \frac{\partial}{\partial x} (e^{x y})

\frac{\partial}{\partial x} (x y cos (3 x)) = y (cos (3 x) - 3 x sin (3 x))

\frac{\partial}{\partial x} (e^{x y}) = e^{x y} y

= y (cos (3 x) - 3 x sin (3 x)) + e^{x y} y

\int e^{3} x d x

\int 2 x e^{- x} d x

a re a 3 (x + 1), 4 (x + 1), x = 7

\int_{0}^{\infty} x e^{- x - y} d x

\int_{0}^{5} \frac{1}{x ^{2} + 25} d x