I have this differential operator $$\frac{d^2}{d y^2}f(y)\qquad (1)$$ I want to make a change of variable $y=x^2$ in $(1)$ so that I get this differential operator $$ \frac{1}{4 x^2} \frac{d^2 }{d x^2}f(x)-\frac{1}{4 x^3}\frac{d}{d x}f(x) \qquad (2)$$

How can I ask Mathematica to do this?

I have this differential operator $$\frac{d^2}{d y^2}\qquad (1)$$ I want to make a change of variable $y=x^2$ in $(1)$ so that I get this differential operator $$ \frac{1}{4 x^2} \frac{d^2 }{d x^2}-\frac{1}{4 x^3}\frac{d}{d x} \qquad (2)$$

How can I ask Mathematica to do this?

I have this differential operator $$\frac{d^2}{d y^2}\qquad (1)$$ I want to make a change of variable $y=x^2$ in $(1)$ so that I get this differential operator $$ \frac{1}{4 x^2} \frac{d^2}{d x^2}-\frac{1}{4 x^3}\frac{d}{d x} \qquad (2)$$

How can I ask Mathematica to do this?

I have this differential operator $$\frac{d^2}{d y^2}f(y)\qquad (1)$$ I want to make a change of variable $y=x^2$ in $(1)$ so that I get this differential operator $$ \frac{1}{4 x^2} \frac{d^2 }{d x^2}f(x)-\frac{1}{4 x^3}\frac{d}{d x}f(x) \qquad (2)$$

How can I ask Mathematica to do this?