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Learn how to solve problems step by step online. Find the implicit derivative d/dx(e^(2xy)=ln(x^1/2)^e^y). Simplify the derivative by applying the properties of logarithms. Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable. Applying the derivative of the exponential function. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function.