(\partial)/(\partial x)(xe^{4x+2y})

Lösung

\frac{\partial}{\partial x} (x e^{4 x + 2 y})

e^{4 x + 2 y} + 4 e^{4 x + 2 y} x

Schritte zur Lösung

\frac{\partial}{\partial x} (x e^{4 x + 2 y})

Behandle

y

als Konstante

Wende die Produktregel an:

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

f = x, g = e^{4 x + 2 y}

= \frac{\partial}{\partial x} (x) e^{4 x + 2 y} + \frac{\partial}{\partial x} (e^{4 x + 2 y}) x

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

\frac{\partial}{\partial x} (e^{4 x + 2 y}) = e^{4 x + 2 y} \cdot 4

= 1 \cdot e^{4 x + 2 y} + e^{4 x + 2 y} \cdot 4 x

Vereinfache

= e^{4 x + 2 y} + 4 e^{4 x + 2 y} x

\int \frac{1}{6 + 2 x} d x

\frac{d}{d x} ((x^{5} + 2)^{2} (x^{3} + 4)^{4})

n = 4 \sum \infty 3 (- \frac{1}{2})^{n}

x \to 0 lim (x^{\frac{1}{3}})

t an g e n t (x^{2} + y^{2})^{2} = 4 x^{2} y, (1, 1)