(\partial)/(\partial x)(xsqrt((4-x^2)))

解

\frac{\partial}{\partial x} (x (4 - x^{2}))

\frac{- 2 x ^{2} + 4}{4 - x ^{2}}

解答ステップ

\frac{\partial}{\partial x} (x (4 - x^{2}))

積の法則を適用:

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

f = x, g = 4 - x^{2}

= \frac{\partial}{\partial x} (x) 4 - x^{2} + \frac{\partial}{\partial x} (4 - x^{2}) x

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

\frac{\partial}{\partial x} (4 - x^{2}) = - \frac{x}{4 - x ^{2}}

= 1 \cdot 4 - x^{2} + (- \frac{x}{4 - x ^{2}}) x

簡素化

1 \cdot 4 - x^{2} + (- \frac{x}{4 - x ^{2}}) x : \frac{- 2 x ^{2} + 4}{4 - x ^{2}}

= \frac{- 2 x ^{2} + 4}{4 - x ^{2}}