(\partial)/(\partial x)(sqrt(x^2+16))

解

\frac{\partial}{\partial x} (x^{2} + 16)

\frac{x}{x ^{2} + 16}

解答ステップ

\frac{\partial}{\partial x} (x^{2} + 16)

連鎖法則を適用:

\frac{1}{2 x ^{2} + 16} \frac{\partial}{\partial x} (x^{2} + 16)

= \frac{1}{2 x ^{2} + 16} \frac{\partial}{\partial x} (x^{2} + 16)

\frac{\partial}{\partial x} (x^{2} + 16) = 2 x

= \frac{1}{2 x ^{2} + 16} \cdot 2 x

簡素化

\frac{1}{2 x ^{2} + 16} \cdot 2 x : \frac{x}{x ^{2} + 16}

= \frac{x}{x ^{2} + 16}