Question

Can someone help me with this

if xy=4 then what is d²y/dx² × d²x/dy²
please read carefully there not the same so they don't equal one ​

Answer 1

Actually, this is equal to 1.

Explanation:

Hello, please consider the following.

First of all, we assume x and y different from 0.

`xy=4\\\\y=(4)/(x)\\\\x=(4)/(x)\\\\\text{So}\\\\y'(x)=(-4)/(x^2)\\\\y''(x)=(-4*(-2))/(x^3)=(8)/(x^3)\\\\x''(y)=(8)/(y^2)\\\\\text{So, we can conclude}`

`(d^2y)/(dx^2)\cdot (d^2x)/(dy^2)=(8)/(x^3)\cdot(8)/(y^3)\\\\=(64)/((xy)^3)\\\\\text{We replace xy by 4}\\\\=(64)/(4^3)\\\\=(64)/(64)\\\\=\large \boxed{\sf \bf \ 1 \ }`

Thank you