Unit Tangent for a Curve: Finding T(t) using the Product Rule

[withthemotive]

Homework Statement

r(t) = 〈sin(t) − t cos(t), cos(t) +t sin(t), 5 t2 + 7 〉

Find the unit tangent. T(t)=

The Attempt at a Solution

r'(t) = <cos(t) + tsin(t), -sin(t) + tcos(t), 10t>

T(t) = r'(t)/ |r'(t)|

|r(t)| = sqrt( 1 + 101t^2)

And so on.
Supposably according to the homework I'm wrong, completely wrong.

 

[Dick]

Your derivative is wrong, completely wrong. You aren't using the product rule.