How do you find the rate of change?

The rate of change is looking for the amount something would change per unit of time (seconds usually)

This can often be found by dividing what you are changing by how long it takes to change (dividing by the time)

If I had a bath tub with a hole in it with water falling out we could find the rate of change of the amount water in the bath tub

If the bath tub started with 100 litres and lost 30 litres in 1 minute

We could do 30 litres divided by 60 seconds giving a rate of change of 0.5 litres per second

I hope this helps!

Hi Vickie!

The rate of change of a system can be found in several different ways depending on the particulars of the question. For this answer, I will assume you're comfortable with single differentiation, and we will talk about some of the cases where there are several derivatives at play! If you would like help with single derivatives for rates of change, then please follow this reply up with another question :)

The crucial thing to ask ourselves is on what conditions (also known as "independent variables") does whatever we are measuring (our "dependent variable") depend on? Here is a quick scheme and example for the rate of change of a dependent variable which depends on two factors:

Let V be the volume of a cuboid with a square base with sides of length x meters, and a height of y meters. Then from geometry we know the volume is given by

V(x,y) = y*(x^2),

where we write V(x,y) because V depends on both x and y, and x^2 is typed notation for x squared. Now if we change x by a small amount, how does this affect V? This is of course a lengthier way of asking: what is the rate of change of V with respect to x? We can calculate this with a derivative, which measures precisely this! If we remember our differentiation, we get:

The rate of change of V with respect to x is given by:

dV/dx = 2xy.

The rate of change of V with respect to y is given by:

dV/dy = x^2.

Now, what if both x and y are changing at the same time? Then we need to consider a global rate of change (which we will label dV/dt), and this is where things get a bit tricky. In summary, we will add together both rates of change! However, we need to be careful to account for how fast x and y are both changing.

Let's pretend that x changes at a rate of 1meter per second, and y changes at a rate of 2meters per second. Then if we add the rates of change, we get:

dV/dt = x^2 + 2xy,

but this is not the whole story! As y is changing at double the speed than x, intuitively we should make sure that the term dV/dy has double the effect on the global rate of change. The correct answer is therefore:

dV/dt = x^2 + 4xy.

This example illustrates an intuitive approach to how rates of change work with several moving parts. The topic called implicit differentiation then takes these ideas and makes them much more automatic! In summary,

The global rate of change is found by multiplying the individual rate of change of each variable by how fast that variable is changing, and adding all these terms together for all independent variables.

Hope this helps!

Alberto

The rate of change is difference of y divided by difference of x. In other words it is the derivative at a given point.

the change in y-values by the change in x-values.

Linear functions have a constant rate of change which is represented as the gradient of the graph.

It is simply the change of y-values with respect to x-values i.e. (y1-y2) / (x1-x2) where (x1,y1), (x2,y2) are the coordinates

You would have to differentiate

The rate of change in measured the change in Y over the change in X

Divide the change of one variable with the change of the other variable

How do find the rate of change

Rate of change is how quickly a measured quantity (e.g. speed) changes in time. To calculate this you need the change in the quantity (e.g. change in speed = final speed - initial speed) and then you need to divide that result by the change in time i.e. the time over which the measured quantity has changed.

E.g. to calculate the acceleration (rate of change of speed) of a car going from 5m/s to 10m/s in 20s you would do:

Acceleration = (10-5)/20 = 0.25m/s^2

The rate of change can be defined by the following formula

rate of change = (change in quantity 1) / (change in quantity 2).

An example is the distance travelled by a car in a certain amount of time.

For a linear set of values the rate of change will be the change in y-values divided by the change in x-values in other words the gradient of a straight line. In the set of values relating to a curved line the rate of change on each point can be found by differentiating the equation of that curve and using the values of x of the point you need to find the rate of change at.

The rate of change measures how a quantity changes over time or across space. It's often represented as the slope of a line connecting two points on a graph.

Rate of change can be calculated by the amount of a specific quantity is changing by the time it took for the change to hapen. A common example in physics in speed which is simply rate of change of position(or distance). If a car changes its position by 20 miles in 30 minnutes then its average speed(or rate of change of position) is 20miles divided by 30min(or 0.5 hr) which is 40 miles per hr

Hi Vickie,

The rate of change is usually obtained if you divide by time.