- #1

hoffmann

- 70

- 0

F(z,w) = f(g_1(z,w),g_2(z,w),z,w)

where f(x,y,z,w)=x^2 +y^2 +z^2 −w^2

and g_1(z,w) = wcosz , g_2(z,w) = wsinz

Evaluate the partials at z = 0, w = 1. Confirm your result by writing out F explicitly as a function of z and w, computing its partial derivatives, and then evaluating at the same point.

I'm a little confused by the differentiation here:

so x = wcosz, y = wsinz thus:

x^2 = w^2cos^z

y^2 = w^2sin^2z

z = z^2

w = -w^2

what next?