Determine the directional derivative of the function \(f(x, y, z) = x^2y^2z^2\) at the point (1, 1, -1) in the direction of the tangent to the curve defined by:
- \(x = e^t\)
- \(y = \sin(2t) + 1\)
- \(z = 1 - \cos(t)\)
at t = 0 .
1
\( \frac{6}{\sqrt{5}} \)
2
\( \frac{5}{\sqrt{6}} \)
3
\( \frac{3}{\sqrt{5}} \)
4
\( \frac{5}{\sqrt{3}} \)