(\partial)/(\partial x)(xe^{2xy})

Lösung

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

e^{2 x y} + 2 e^{2 x y} x y

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Produktregel an:

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

f = x, g = e^{2 x y}

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

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

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

= 1 \cdot e^{2 x y} + e^{2 x y} \cdot 2 y x

Vereinfache

= e^{2 x y} + 2 e^{2 x y} x y

x y^{2} \frac{d y}{d x} = y^{3} - x^{3}, y (1) = 1

d er i v a t i v e f (x) - 2 x^{2}

\frac{\partial}{\partial x} (x^{2} y - x y^{2})

t an g e n t f (x) = 2 x + 3, (3, 3)

d er i v a t i v e y = 6 ln (x) - x^{3} + 2 3 x