What is (\partial ^2)/(\partial y^2)(ln(2+x^2y^2)) ?

The answer to (\partial ^2)/(\partial y^2)(ln(2+x^2y^2)) is (2x^2(2-x^2y^2))/((2+x^2y^2)^2)

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

\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}}

Solution steps

\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}}

What is (\partial ^2)/(\partial y^2)(ln(2+x^2y^2)) ?
The answer to (\partial ^2)/(\partial y^2)(ln(2+x^2y^2)) is (2x^2(2-x^2y^2))/((2+x^2y^2)^2)