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Is it possible to determine dy/dx given that e^(x*y) - x*y = y

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torrip996 | Student, Grade 10 | Salutatorian

Posted September 11, 2013 at 4:19 PM via web

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Is it possible to determine dy/dx given that e^(x*y) - x*y = y

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted September 11, 2013 at 4:25 PM (Answer #1)

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The derivative `dy/dx` has to be determined given that` e^(x*y) - x*y = y` .

Use implicit differentiation,

`(d(e^(x*y) - x*y))/dx = dy/dx`

=> `e^(x*y)*(y + dy/dx) - dy/dx - y = dy/dx`

=> `(dy/dx)(e^(x*y) - 2) = y - y*e^(x*y)`

=> `dy/dx = (y - y*e^(x*y))/(e^(x*y) - 2)`

The derivative `dy/dx = (y - y*e^(x*y))/(e^(x*y) - 2)`

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