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

解

\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)

解答ステップ

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

y, z

を定数として扱う

定数を除去:

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

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

積の法則を適用:

(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)