Questions: Differentiate the function f(t) = t^(2/2)(11t+8).

Transcript text: Differentiate the function $f(t)=t^{\frac{2}{2}}(11 t+8)$.

Solution

Solution Steps

Step 1: Simplify the Function

The given function is $ f(t) = t^{\frac{2}{2}}(11t + 8) $. Simplifying the exponent, we have: \[ f(t) = t(11t + 8) \]

Step 2: Differentiate the Function

To differentiate $ f(t) $, we apply the product rule. Let:

$ u(t) = t $
$ v(t) = 11t + 8 $

Calculating the derivatives:

$ u'(t) = 1 $
$ v'(t) = 11 $

Using the product rule: \[ f'(t) = u'(t)v(t) + u(t)v'(t) = 1 \cdot (11t + 8) + t \cdot 11 \] This simplifies to: \[ f'(t) = 11t + 8 + 11t = 22t + 8 \]

Final Answer

The derivative of the function $ f(t) $ is: \[ \boxed{f'(t) = 22t + 8} \]

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