(\partial)/(\partial x)(sqrt(20-4x^2-3y^2))

解

\frac{\partial}{\partial x} (20 - 4 x^{2} - 3 y^{2})

- \frac{4 x}{20 - 4 x ^{2} - 3 y ^{2}}

解答ステップ

\frac{\partial}{\partial x} (20 - 4 x^{2} - 3 y^{2})

y

を定数として扱う

連鎖法則を適用:

\frac{1}{2 20 - 4 x ^{2} - 3 y ^{2}} \frac{\partial}{\partial x} (20 - 4 x^{2} - 3 y^{2})

= \frac{1}{2 20 - 4 x ^{2} - 3 y ^{2}} \frac{\partial}{\partial x} (20 - 4 x^{2} - 3 y^{2})

\frac{\partial}{\partial x} (20 - 4 x^{2} - 3 y^{2}) = - 8 x

= \frac{1}{2 20 - 4 x ^{2} - 3 y ^{2}} (- 8 x)

簡素化

\frac{1}{2 20 - 4 x ^{2} - 3 y ^{2}} (- 8 x) : - \frac{4 x}{20 - 4 x ^{2} - 3 y ^{2}}

= - \frac{4 x}{20 - 4 x ^{2} - 3 y ^{2}}