How can I find the stationary point of y = e^2x cos x?

At a stationary point of y, dy/dx = 0.Step 1: Let's find dy/dx first by differentiating. To differentiate the product of two functions, we can use the product rule:d(fg)/dx = f * dg/dx + df/dx * g. So dy/dx = d(e^2x cos x)/dx = (e^2x) * (-sin x) + (2e^2x) * cos x = 2e^2x cos x - e^2x sin x.Step 2: Now we've found dy/dx, we can set it to 0. So we can set 2e^2x cos x - e^2x sin x = 0. Therefore 2e^2x cos x = e^2x sinx. We can cancel e^2x from each side because it is never equal to zero, therefore 2cos x = sin x. Dividing by cos x gives 2 = tan x. We can use arctan now to find x: arctan 2 = arctan(tan x) = x. Now finally we know x, so we can find y by plugging into our original equation: y = e ^ (2*arctan2) * cos (arctan2) = 4.09