differentiate g(t)=3t/2t+1

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}