(\partial)/(\partial x)(xexp(x,y,z)(-x^2-y^2-z^2))

Lösung

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

e (1 \cdot x p (x, y, z) (- x^{2} - y^{2} - z^{2}) + (1 \cdot p (x, y, z) (- x^{2} - y^{2} - z^{2}) + (\frac{\partial}{\partial x} (p (x, y, z)) (- x^{2} - y^{2} - z^{2}) + (- 2 x) p (x, y, z)) x) x)

Schritte zur Lösung

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

Behandle

y, z

als Konstanten

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= e \frac{\partial}{\partial x} (xx p (x, y, z) (- x^{2} - y^{2} - z^{2}))

Wende die Produktregel an:

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

f = x, g = x p (x, y, z) (- x^{2} - y^{2} - z^{2})

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

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

\frac{\partial}{\partial x} (x p (x, y, z) (- x^{2} - y^{2} - z^{2})) = 1 \cdot p (x, y, z) (- x^{2} - y^{2} - z^{2}) + (\frac{\partial}{\partial x} (p (x, y, z)) (- x^{2} - y^{2} - z^{2}) + (- 2 x) p (x, y, z)) x

= e (1 \cdot x p (x, y, z) (- x^{2} - y^{2} - z^{2}) + (1 \cdot p (x, y, z) (- x^{2} - y^{2} - z^{2}) + (\frac{\partial}{\partial x} (p (x, y, z)) (- x^{2} - y^{2} - z^{2}) + (- 2 x) p (x, y, z)) x) x)

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