(\partial)/(\partial x)(rsqrt((g(r,x))/(2h)))

解

\frac{\partial}{\partial x} (r \frac{g ( r , x )}{2 h})

r \frac{1}{2 \frac{g ( r , x )}{2 h}} \cdot \frac{1}{2 h} \frac{\partial}{\partial x} (g (r, x))

解答ステップ

\frac{\partial}{\partial x} (r \frac{g ( r , x )}{2 h})

h, r

を定数として扱う

定数を除去:

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

= r \frac{\partial}{\partial x} (\frac{g ( r , x )}{2 h})

連鎖法則を適用:

\frac{1}{2 \frac{g ( r , x )}{2 h}} \frac{\partial}{\partial x} (\frac{g ( r , x )}{2 h})

= \frac{1}{2 \frac{g ( r , x )}{2 h}} \frac{\partial}{\partial x} (\frac{g ( r , x )}{2 h})

\frac{\partial}{\partial x} (\frac{g ( r , x )}{2 h}) = \frac{1}{2 h} \frac{\partial}{\partial x} (g (r, x))

= r \frac{1}{2 \frac{g ( r , x )}{2 h}} \cdot \frac{1}{2 h} \frac{\partial}{\partial x} (g (r, x))