You're almost right, for each partial derivative you MUST use the product rule, for example:
You have to differentiate them as such to arrive at answers that you can use for the CR equations.
u(x,y) = cos(4xy)e^(2x² - 2y² + 2)
v(x,y) = sin(4xy)e^(2x² - 2y² + 2)
Compute the partial derivatives of u and v with respect to x and y for all values (x, y) and verify that they satisfy the Cauchy-Riemann equations.
How do I differentiate each?
for example i got du/dx=4e^(2x² - 2y² + 2)cos(4xy)
du/dy=4ye^(2x² - 2y² + 2)cos(4xy)
dv/dx=4e^(2x² - 2y² + 2)sin(4xy)
dv/dy=4ye^(2x² - 2y² + 2)sin(4xy)
Im not sure if this is correct