(\partial)/(\partial x)(e^{3x^2y}(1+x-2y))

Lösung

\frac{\partial}{\partial x} (e^{3 x^{2} y} (1 + x - 2 y))

6 e^{3 x^{2} y} x y (1 + x - 2 y) + e^{3 x^{2} y}

Schritte zur Lösung

\frac{\partial}{\partial x} (e^{3 x^{2} y} (1 + x - 2 y))

Behandle

y

als Konstante

Wende die Produktregel an:

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

f = e^{3 x^{2} y}, g = 1 + x - 2 y

= \frac{\partial}{\partial x} (e^{3 x^{2} y}) (1 + x - 2 y) + \frac{\partial}{\partial x} (1 + x - 2 y) e^{3 x^{2} y}

\frac{\partial}{\partial x} (e^{3 x^{2} y}) = e^{3 x^{2} y} \cdot 6 y x

\frac{\partial}{\partial x} (1 + x - 2 y) = 1

= e^{3 x^{2} y} \cdot 6 y x (1 + x - 2 y) + 1 \cdot e^{3 x^{2} y}

Vereinfache

= 6 e^{3 x^{2} y} x y (1 + x - 2 y) + e^{3 x^{2} y}

\frac{d}{d x} (9 - 4 x)

\int π (x + 1)^{2} d x

(x, y) \to (0, 9) lim (x^{3} y)

\frac{\partial}{\partial x} (e^{x \cdot c o s (y)})

l a pl a ce t r an s f or m - 5 (t - 2) e^{t - 2}