What is expand (d^2)/(d^2x)(x^2+y^2=1) ?

The solution to expand (d^2)/(d^2x)(x^2+y^2=1) is x+(y^2)/x =1

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expand (d^2)/(d^2x)(x^2+y^2=1)

expand

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

x + \frac{y ^{2}}{x} = 1

Solution steps

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

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

Apply the distributive law:

a (b + c) = ab + a c

a = \frac{d ^{2}}{d ^{2} x}, b = x^{2}, c = y^{2} = 1

\frac{d ^{2}}{d ^{2} x} x^{2} + \frac{d ^{2}}{d ^{2} x} y^{2} = 1

Expand

\frac{d ^{2}}{d ^{2} x} x^{2} + \frac{d ^{2}}{d ^{2} x} y^{2} : x + \frac{y ^{2}}{x}

x + \frac{y ^{2}}{x} = 1

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What is expand (d^2)/(d^2x)(x^2+y^2=1) ?
The solution to expand (d^2)/(d^2x)(x^2+y^2=1) is x+(y^2)/x =1