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Find `dy/dx` for cos(y^2) + x = e^y

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l0932 | Student, Undergraduate | eNotes Newbie

Posted March 13, 2012 at 10:59 PM via web

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Find `dy/dx` for cos(y^2) + x = e^y

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted March 13, 2012 at 11:13 PM (Answer #1)

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The derivative `dy/dx` has to be determined for `cos(y^2) + x = e^y`

Using implicit differentiation gives:

`-sin(y^2)*2y*(dy/dx) + 1 = e^y*(dy/dx)`

=> `(dy/dx)*(e^y + sin(y^2)*2y) = 1`

=> `dy/dx = 1/(e^y + sin(y^2)*2y)`

The derivative `dy/dx` for the expression `cos(y^2) + x = e^y` is `dy/dx = 1/(e^y + sin(y^2)*2y)`

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