(\partial)/(\partial x)((((x+4))/(y+5))^{1/2})

解

\frac{\partial}{\partial x} ((\frac{( x + 4 )}{y + 5})^{\frac{1}{2}})

\frac{1}{2 ( x + 4 ) ^{\frac{1}{2}} ( y + 5 ) ^{\frac{1}{2}}}

解答ステップ

\frac{\partial}{\partial x} ((\frac{( x + 4 )}{y + 5})^{\frac{1}{2}})

y

を定数として扱う

連鎖法則を適用:

\frac{1}{2 ( \frac{x + 4}{y + 5} ) ^{\frac{1}{2}}} \frac{\partial}{\partial x} (\frac{x + 4}{y + 5})

= \frac{1}{2 ( \frac{x + 4}{y + 5} ) ^{\frac{1}{2}}} \frac{\partial}{\partial x} (\frac{x + 4}{y + 5})

\frac{\partial}{\partial x} (\frac{x + 4}{y + 5}) = \frac{1}{y + 5}

= \frac{1}{2 ( \frac{x + 4}{y + 5} ) ^{\frac{1}{2}}} \cdot \frac{1}{y + 5}

簡素化

\frac{1}{2 ( \frac{x + 4}{y + 5} ) ^{\frac{1}{2}}} \cdot \frac{1}{y + 5} : \frac{1}{2 ( x + 4 ) ^{\frac{1}{2}} ( y + 5 ) ^{\frac{1}{2}}}

= \frac{1}{2 ( x + 4 ) ^{\frac{1}{2}} ( y + 5 ) ^{\frac{1}{2}}}