(\partial)/(\partial x)(x(1-x^2-y^2))

解

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

- 3 x^{2} - y^{2} + 1

解答ステップ

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

y

を定数として扱う

積の法則を適用:

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

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

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

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

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

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

簡素化

1 \cdot (1 - x^{2} - y^{2}) + (- 2 x) x : - 3 x^{2} - y^{2} + 1

= - 3 x^{2} - y^{2} + 1