(\partial)/(\partial y)(1/(t(y^2-9)))

解

\frac{\partial}{\partial y} (\frac{1}{t ( y ^{2} - 9 )})

- \frac{2 y}{t ( y ^{2} - 9 ) ^{2}}

解答ステップ

\frac{\partial}{\partial y} (\frac{1}{t ( y ^{2} - 9 )})

t

を定数として扱う

定数を除去:

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

= \frac{1}{t} \frac{\partial}{\partial y} (\frac{1}{y ^{2} - 9})

指数の規則を適用する:

\frac{1}{a} = a^{- 1}

= \frac{1}{t} \frac{\partial}{\partial y} ((y^{2} - 9)^{- 1})

連鎖法則を適用:

- \frac{1}{( y ^{2} - 9 ) ^{2}} \frac{\partial}{\partial y} (y^{2} - 9)

= - \frac{1}{( y ^{2} - 9 ) ^{2}} \frac{\partial}{\partial y} (y^{2} - 9)

\frac{\partial}{\partial y} (y^{2} - 9) = 2 y

= \frac{1}{t} (- \frac{1}{( y ^{2} - 9 ) ^{2}} \cdot 2 y)

簡素化

\frac{1}{t} (- \frac{1}{( y ^{2} - 9 ) ^{2}} \cdot 2 y) : - \frac{2 y}{t ( y ^{2} - 9 ) ^{2}}

= - \frac{2 y}{t ( y ^{2} - 9 ) ^{2}}