I am really struggling with a highschool calculus question which involves finding the derivative of a function using the first principles.
The question is as follows:
Find the derivative of f(x) = (3x-1)/(x+2) when x ≠ -2
I am having trouble with this problem because I am unsure what to do when I have put my function of f(x+h) into the equation f'(x) = [f(x+h)-f(x)]/h.
This is a link so my working so far and I would greatly appreciate it if you could please explain the steps how to finish this question.
http://tinypic.com/view.php?pic=15qqnbn&s=8#.VOq8wPmUePt
Thank you,
Geoffrey
Best Answer
With some tedious algebra you have ${f(x+h)-f(x) \over h} = {7 \over x^2+(h+4)x + 2h +4}$, which is 'nicely' behaved at $h=0$, so we see that $\lim_{h \to 0} {f(x+h)-f(x) \over h} = {7 \over x^2+4x + 4} = {7 \over (x+2)^2 }$.