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

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murciof | Student, College Freshman | eNoter

Posted May 20, 2013 at 12:29 PM via web

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

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pramodpandey | College Teacher | Valedictorian

Posted May 20, 2013 at 1:12 PM (Answer #1)

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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.

 

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