Calculate the derivative of the function y = e^2x.

The derivative of y = e^2x is 2e^2x.

To find the derivative of y = e^2x, we use the chain rule. Let u = 2x, then y = e^u. The chain rule states that the derivative of y with respect to x is the derivative of y with respect to u multiplied by the derivative of u with respect to x.

So,

dy/dx = dy/du * du/dx

We know that dy/du = e^u, and du/dx = 2.

Therefore,

dy/dx = e^u * 2

Substituting back in for u, we get

dy/dx = e^(2x) * 2

Simplifying,

dy/dx = 2e^(2x)

Therefore, the derivative of y = e^2x is 2e^2x.