(\partial)/(\partial x)(-ksqrt(p(x)gx))

解

\frac{\partial}{\partial x} (- k p (x) gx)

- \frac{k g ( x \frac{\partial}{\partial x} ( p ( x ) ) + p ( x ) )}{2 x p ( x )}

解答ステップ

\frac{\partial}{\partial x} (- k p (x) gx)

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= - k \frac{\partial}{\partial x} (p (x) gx)

連鎖法則を適用:

\frac{1}{2 p ( x ) gx} \frac{\partial}{\partial x} (p (x) gx)

= \frac{1}{2 p ( x ) gx} \frac{\partial}{\partial x} (p (x) gx)

\frac{\partial}{\partial x} (p (x) gx) = g (x \frac{\partial}{\partial x} (p (x)) + p (x))

= - k \frac{1}{2 p ( x ) gx} g (x \frac{\partial}{\partial x} (p (x)) + p (x))

簡素化

- k \frac{1}{2 p ( x ) gx} g (x \frac{\partial}{\partial x} (p (x)) + p (x)) : - \frac{k g ( x \frac{\partial}{\partial x} ( p ( x ) ) + p ( x ) )}{2 x p ( x )}

= - \frac{k g ( x \frac{\partial}{\partial x} ( p ( x ) ) + p ( x ) )}{2 x p ( x )}