(\partial ^2)/(\partial y^2)(ln(2+x^2y^2))

解

\frac{\partial ^{2}}{\partial y ^{2}} (ln (2 + x^{2} y^{2}))

\frac{2 x ^{2} ( 2 - x ^{2} y ^{2} )}{( 2 + x ^{2} y ^{2} ) ^{2}}

解答ステップ

\frac{\partial ^{2}}{\partial y ^{2}} (ln (2 + x^{2} y^{2}))

\frac{\partial}{\partial y} (ln (2 + x^{2} y^{2})) = \frac{2 x ^{2} y}{2 + x ^{2} y ^{2}}

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

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

= \frac{2 x ^{2} ( 2 - x ^{2} y ^{2} )}{( 2 + x ^{2} y ^{2} ) ^{2}}