1. ## Derivative problem

I'm finding this calculus problems interesting yet have trouble with a lot of them. hopefully this forum can help me

anyway....there is this derivative problem....

f(x)=x-2/x^2+1 Square root

f(x)=lim f(x-h) - f(x)/h
h>0

f(x)= lim x+h-2/(x+h)^2+1 Square root - x-2/x^2+1 Square root
h>0 /h

man, I hope that's understandable. hopefully someone can teach me how to do square roots and other stuff

just in case, the square roots go in x^2+1, (x+h)^2+1, and x^2+1 which are all denominators. and the h divides everything in the third part

anyway, I do have the answer.... 2x+1/(x^2+1)^3/2

I just don't know how to get there. I know the first step would be to cross multiply the ones in the 3rd part. I get lost after that

2. Do you need to find the derivative of $\displaystyle f(x)=\sqrt\frac{x-2}{x^2+1}$ using limits?

Is this what you meant by your notation?

3. ## Latex

Allow me to help with the typesetting. Learn LaTex for easier communication.

Problem: Derive $\displaystyle f(x)=\frac{x-2}{\sqrt{x^2+1}}$

Definition: $\displaystyle f'(x)=\lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}$

Answer: $\displaystyle \frac{2x+1}{(x^2+1)^{3/2}}$

Just to clarify, are you required to find the answer using this limit definition of the derivative, or by using the easy way?

4. Originally Posted by artvandalay11
Do you need to find the derivative of $\displaystyle f(x)=\sqrt\frac{x-2}{x^2+1}$ using limits?

Is this what you meant by your notation?
yes, thanks

Originally Posted by Media_Man
Allow me to help with the typesetting. Learn LaTex for easier communication.

Problem: Derive $\displaystyle f(x)=\frac{x-2}{\sqrt{x^2+1}}$

Definition: $\displaystyle f'(x)=\lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}$

Answer: $\displaystyle \frac{2x+1}{(x^2+1)^{3/2}}$

Just to clarify, are you required to find the answer using this limit definition of the derivative, or by using the easy way?
umm....I don't know about the easy way. let's start by the normal way, I actually want to learn this stuff

any link to that LaTex btw?

5. any link to that LaTex btw?
Just click on our equations to see the code. It's fairly easy to learn just by doing, especially if you're familiar with programming.

6. Hey dude, check this out:

Latex.pdf (148.9 KB, 871 views)