(\partial)/(\partial x)(xe^{yx^2}sin(x))

Lösung

\frac{\partial}{\partial x} (x e^{y x^{2}} sin (x))

e^{x^{2} y} sin (x) + x (2 e^{x^{2} y} x y sin (x) + e^{x^{2} y} cos (x))

Schritte zur Lösung

\frac{\partial}{\partial x} (x e^{y x^{2}} sin (x))

Behandle

y

als Konstante

Wende die Produktregel an:

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

f = x, g = e^{y x^{2}} sin (x)

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

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

\frac{\partial}{\partial x} (e^{y x^{2}} sin (x)) = e^{y x^{2}} \cdot 2 y x sin (x) + cos (x) e^{y x^{2}}

= 1 \cdot e^{y x^{2}} sin (x) + (e^{y x^{2}} \cdot 2 y x sin (x) + cos (x) e^{y x^{2}}) x

Vereinfache

= e^{x^{2} y} sin (x) + x (2 e^{x^{2} y} x y sin (x) + e^{x^{2} y} cos (x))

\int_{0}^{1} 1

\int \frac{3}{2} d x

x \to 4 lim (x^{2} - x - 12)

\int \frac{1}{( 1 + cos ( x ) )} d x

x \to \infty lim (x (x + 1))