1. Identify functions \( u \) and \( v \):
u = 3t
v = 2t + 1
2. Compute the derivatives:
u' = 3
v' = 2
3. Apply the quotient rule:
g'(t) = \frac{u'v - uv'}{v^2}
g'(t) = \frac{(3)(2t + 1) - (3t)(2)}{(2t + 1)^2}
4. Simplify the expression:
g'(t) = \frac{6t + 3 - 6t}{(2t + 1)^2}
g'(t) = \frac{3}{(2t + 1)^2}
5. The derivative of \( g(t) \) is:
g'(t) = \frac{3}{(2t + 1)^2}