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