# If sqrt((x²)+(y²))=x²y², find (dy)/(dx) ?

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We have given

`sqrt(x^2+y^2)=x^2y^2` (i)

squaring (i) both side

`x^2+y^2=x^4y^4` (ii)

Differentiate (ii) with respect to x implicitly

`2x+2y(dy)/(dx)=4x^3y^4+4x^4y^3(dy)/dx`

`(2y-4x^4y^3)(dy)/(dx)=(4x^3y^4-2x)`

`(dy)/(dx)=(2(2x^3y^4-x))/(2(y-2x^4y^3))`

`(dy)/(dx)=(2x^3y^4-x)/(y-2x^4y^3)```

We have used following rules,

d(f(x).g(x))=d(f(x)). g(x)+ f(x). d(g(x)) -- product rule.