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Problem 33 Hard Difficulty

Find $ f'(a) $.

$ f(t) = \dfrac{2t + 1}{t + 3} $

Answer

$f^{\prime}(a)=\frac{5}{(a+3)^{2}}$

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Video Transcript

So here we give an example of a specific function. We have F F T equals two T plus one over T plus three. And we're asked to find the derivative of this function at a certain point. So this is in quotient rule forms of precaution role. We take the derivative of the first function, multiplied by the second function and change time. The jury live of the second function multiplied by the first function unchanged, divided by the square root of our second function squared. So this would be equivalent to two times T plus three -2, T Plus one divided by T plus three squared. The two teas cancel out. So this would be in the end just 6 -1, which would be five over T plus three squared. And we're asked to find the derivative when our time is equivalent to a. So this would be five divided by a plus three squared, which is also a colon, 25 divided by a squared plus six A plus nine. And this is our final answer.