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

解

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

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

解答ステップ

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

定数を除去:

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

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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