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Find dy/dx : x^3+y^3=18y
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We have to find dy/dx given that x^3+y^3=18y
x^3 + y^3 = 18*y
Using implicit differentiation gives:
[x^3 + y^3]' = [18*y]'
=> [x^3]' + [y^3]' = [18*y]'
=> 3x^2 + 3y^2*y' = 18*y'
=> y'(18 - 3y^2) = 3x^2
=> y' = 3x^2/(18 - 3y^2)
The required value of dy/dx = 3x^2/(18 - 3y^2)
Posted by justaguide on October 19, 2011 at 12:52 AM (Answer #1)
x^3 + y^3 = 18 y
3x^2 + 3y^2 dy/dx = 18 dy/dx
3x^2 = 18 dy/dx - 3y^2 dy/dx
3x^2 = dy/dx (18-3y^2)
(3x^2)/(18-3y^2) = dy/dx
Posted by rubeus-hagrid on October 19, 2011 at 1:15 AM (Answer #2)
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