We're using Euler's Formula to rotate a coordinate system. The problem is asking me to show that the gradients of the function have the same length. I have the coordinates x,y on the normal axis and X,Y on the rotated axis.

$\displaystyle

x = Xcos(t) - Ysin (t)

$

$\displaystyle

y = Xsin(t) + Ycos(t)

$

I know to find the length of the gradient would be the square root of each derivative squared. Just a little confused what I should use as the derivatives. Thanks.