(\partial)/(\partial x)(54-2/3 x^2-4y^2)

解

\frac{\partial}{\partial x} (54 - \frac{2}{3} x^{2} - 4 y^{2})

- \frac{4 x}{3}

解答ステップ

\frac{\partial}{\partial x} (54 - \frac{2}{3} x^{2} - 4 y^{2})

簡素化

54 - \frac{2}{3} x^{2} - 4 y^{2} : 54 - \frac{2 x ^{2}}{3} - 4 y^{2}

= \frac{\partial}{\partial x} (54 - \frac{2 x ^{2}}{3} - 4 y^{2})

y

を定数として扱う

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (54) - \frac{\partial}{\partial x} (\frac{2 x ^{2}}{3}) - \frac{\partial}{\partial x} (4 y^{2})

\frac{\partial}{\partial x} (54) = 0

\frac{\partial}{\partial x} (\frac{2 x ^{2}}{3}) = \frac{4 x}{3}

\frac{\partial}{\partial x} (4 y^{2}) = 0

= 0 - \frac{4 x}{3} - 0

簡素化

= - \frac{4 x}{3}