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Explaining the Derivative
Thomas R. ... Unfortunately for him, he missed class last week when the professor was explaining the derivative. Since Jimmy feels very guilty about missing class, he came to me, a math major, for a written explanation of the derivative. ...
1 Introduction
Jimmy, the concept of the derivative is very important in mathematics. ... Problems seeking velocity, acceleration, average rate of change, maximum profit, and minimal loss are but a few examples of the application of the derivative.
2 Explanation
The best way that I can describe a derivative is that it represents the slope of the line tangent to a point on a graph. ... By taking the derivative of the function
y = f(x) = x2,
we can simply plug in a value for x and find the desired slope.
But what IS the derivative? ...
This above equation, which further will be referred to as Equation 1, is exactly the definition of a derivative! Simply use this equation for any function f(x) and you will have the derivative for that function. ...
Allow me to demonstrate finding the derivative of y = x2 numerically. Earlier, I said that the derivative of this equation at point (1,1) is 2. Observe:
The derivative of f(x) =
=
=
=
=
=
, since h approaches zero.
Approximate Word count = 1027
Approximate Pages = 4.1
(250 words per page double spaced)
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