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Hello, this question is really giving me some trouble (I'm a super-nerd, I guess, working ahead in my textbook for fun). It is:

Given f(x)= 2x/(5x^(2)-x)

Find the instantaneous rate of change when x=3

Thanks!

It will be simpler to take the derivative if you reduce the function:

f(x) = 2x/(5x²-x) = 2/(5x-1) = 2(5x-1)⁻¹

That way, you don't have to use the quotient rule.

f'(x) = -10/(5x-1)²:

https://www.flickr.com/photos/dwread/15789825509/

Instantaneous rate of change when x=3:

f'(3) = -10/(5·3-1)² = -5/98

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