
[SOLVED] Differentiation
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 CauchyRiemann 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

You're almost right, for each partial derivative you MUST use the product rule, for example:
$\displaystyle \frac{\partial{u}}{\partial{x}} = \frac{\partial{[\cos{(4xy)}]}}{\partial{x}}e^{(2x^2  2y^2  2)} + \cos{(4xy)}\frac{\partial{[e^{(2x^2  2y^2  2)}}]}{\partial{x}}$
$\displaystyle = 4\sin{(4xy)}e^{(2x^2  2y^2  2)} + 4x\cos{(4xy)}e^{(2x^2  2y^2  2)}$
$\displaystyle = 4e^{(2x^2  2y^2  2)}[x\cos{(4xy)}  \sin{(4xy)}]$
You have to differentiate them as such to arrive at answers that you can use for the CR equations.