Math CentralQuandaries & Queries


Question from Meagan, a student:

Using the limit definition find the derivative of 3/(2x^2)

Hi Meagan,

Let me try a slightly different problem

Using the limit definition find the derivative of f(x) = 4/(5x3).

The limit definition of the derivative is


With my function the numerator of the limit fraction is


Factor the numerator of this expression as a difference of cubes and simplify. You will find a factor of -h. Now divide by h to obtain

limit fraction.

Simplify. There is no longer an h in the denominator and you can see the result of taking the limit as h approaches zero.

I hope this helps,

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