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The derivative, or rate of change, of
a function is another function that gives the value of the slope at
every point on the x axis of the original function. There is more
than one way to write the derivative, but we will stick with dy over dx
for this exercise. |
| It is fairly simple to find the
derivative of simple equations. First you bring the exponent down
and multiply it by the coefficient. Then you take the previous
exponent and subtract that by 1. This is now the new exponent.
This new function is the derivative. |
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Example: We start of with 3
times x squared. We bring down the exponent of 2 and multiply that
by 3. We then subtract the exponent, 2, by 1. The new
exponent is now 1. We now end up with 6x as the derivative. |
| Graph: This is the graph of the
function, y = 3x2. |
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| Graph: This is the graph of y
= 6x. As you can see this graph follows the slope of y = 3x2.
Where the slope is a big positive number in the graph above, the y in
the graph below is a big positive number. They match up perfectly. |
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