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The relative rate of change of $y=f(x)$ with respect to $x$ at $x=a$ is defined by $\frac{f^{\prime}(a)}{f(a)}$. Find the relative rate of change of $f(x)$ with respect to $x$, (or $f(t)$ with respect to $t$ ).$$f(x)=\sqrt{\frac{x+3}{x-2}}, \quad a=6$$

$$-5 / 72$$

Calculus 1 / AB

Chapter 2

An Introduction to Calculus

Section 7

Marginal Functions and Rates of Change

Derivatives

Campbell University

University of Michigan - Ann Arbor

Boston College

Lectures

04:40

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.

30:01

In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (the rate of change of the value of the function). If the derivative of a function at a chosen input value equals a constant value, the function is said to be a constant function. In this case the derivative itself is the constant of the function, and is called the constant of integration.

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Okay, So this question wants us to find the relative rate of change, which is the derivative divided by the function for this function, F a T. So we're gonna have to calculate the derivative so f prime of tea. It's just well, the six stays out in front and then using the power rule on that it's just too t or f. Crime of tea equals 12 t when we simplify everything out. So now we can just plug into our formula here. We're curious to see what f crime of tea divided by half of T is equal to. And in our case, we said F prime of tea was 12 t and then f of tea was 60 square, and this works out to be two divided by T, and that's our answer.

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