I'm trying to compute the (implicit) derivative dy/dx from the function e^(2y)=x^3 If I use ln on both sides I can isolate y and find the derivative: ln(e^(2y))=ln(x^3) 2y=3ln(x) y=3/2 ln(x) y′=3/2x But if I use implicit differentiation I get: d/dx(e^(2y))=d/dx x^3 d/dy(e^(2y))d/dx(y)=3x^2 2e^(2y)⋅y′=3x^2 y′=(3x^2)/(2e^(2y)) I know both methods should give the same result. What am I missing?

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