Finding the principal unit normal vector

[spacewater]

r(t) = 3ti+2t^2j

T(t) = 1/(9+16t^2)^-1/2 x (3i + 4tj)

T '(t) = 1/(9+16t^2)^-1/2 x (4j) - 16t/(9+16t^2)^-3/2 x (3i + 4tj)

= 12/(9+16t^2)^-3/2 x (-4ti + 3j) <<<<<------------- I dont understand how this can be derived from the equation above. Can someone please explain to me? x means multiplication

 

[galactus]

The principal unit normal vector is:

\(\displaystyle \frac{T'(t)}{||T'(t)||}\)

The algebra may be messy, but you have the info there. Find the norm of \(\displaystyle T'(t)\)