1. ## Polynomial Simplification

First time poster here!

I am reading through some calculus proofs on derivatives and I'm a little rusty on some of my algebra. Would someone mind helping me figure out the steps to go from #1 to #2?

#1 $\displaystyle (x+dx)^{-2}$

#2 $\displaystyle x^{-2}*(1+\frac{dx}{x})^{-2}$

I would like to politely request a step by step answer if you wouldn't mind because i don't remember much about this from Algebra. You will not insult my intelligence. Thanks in advance for your help.

-db

2. Originally Posted by dbakeg00
First time poster here!

I am reading through some calculus proofs on derivatives and I'm a little rusty on some of my algebra. Would someone mind helping me figure out the steps to go from #1 to #2?

#1 $\displaystyle (x+dx)^{-2}$

#2 $\displaystyle x^{-2}*(1+\frac{dx}{x})^{-2}$

To $\displaystyle \frac{1}{(x+ dx)^2}= \frac{1}{x^2+ 2x dx+ (dx)^2}$
Start buy factoring an "x" out of (x+ dx): since $\displaystyle dx= x\frac{dx}{x}$ that is $\displaystyle x(1+ \frac{dx}{x})$

Now take both to the -2 power: $\displaystyle x^{-2}(1+ \frac{dx}{x})^{-2}$

I would like to politely request a step by step answer if you wouldn't mind because i don't remember much about this from Algebra. You will not insult my intelligence. Thanks in advance for your help.

-db

3. Thank you.

I guess I never knew that $\displaystyle dx= x\frac{dx}{x}$...that must be why I couldn't see how you got from the first expression to the second. That helped a lot. Thank you again.

db

4. Anyone care to explain why $\displaystyle dx= x\frac{dx}{x}$...I'm not sure I remember that

thanks,
db

5. You cancel the two "x"s. You learned that in the third grade.