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Find $ f'(a) $.

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

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

04:34

Daniel Jaimes

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 7

Derivatives and Rates of Change

Limits

Derivatives

Campbell University

Harvey Mudd College

University of Nottingham

Idaho State University

Lectures

04:40

In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

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03:54

Find $$f^{\prime}(a)$$…

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Find $f^{\prime}(a)$.$…

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Find $f^{\prime \prime}(a)…

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Find $ f $.

$ f&#x…

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$ f&qu…

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04:48

Find either $F(s)$ or $f(t…

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.

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