Find dy/dx by implicit differentiation. e^(x/y) = 5x-y

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The value of `dy/dx` has to be determined for `e^(x/y) = 5x-y` . Using implicit differentiation gives

`e^(x/y)/y^2*(y - x*(dy/dx)) = 5 - dy/dx`

=> `(dy/dx)((x*e^(x/y))/y^2 + 1) = 5 - e^(x/y)/y`

=> `(dy/dx) = (5 - e^(x/y)/y)/((x*e^(x/y))/y^2 + 1)`

The required derivative `(dy/dx) = (5 - e^(x/y)/y)/((x*e^(x/y))/y^2 + 1)`

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