Question

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

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Jon

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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}

2. Compute the derivatives:

3. Apply the quotient rule:

4. Simplify the expression:

5. The derivative of \( g(t) \) is:

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