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

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

1 \cdot e^{x^{2} - y} + e^{x^{2} - y} \cdot 2 xx : e^{x^{2} - y} + 2 e^{x^{2} - y} x^{2}

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

\int (x + 2) (3 x^{2} + 12 x) d x

\frac{\partial}{\partial y} (x y^{2} + y e^{x^{2}} + 5)

d er i v a t i v e y = ln (x + 5)

x \to 2 lim (x^{2} + 6)

d er i v a t i v e \frac{( 4 x ^{2} + 4 x + 6 )}{x}