1. ## Differential Equations...

Use the definition of the derivative to find f' (x).

f (x)= $\displaystyle \frac {1}{x^2}$

f'(x)= $\displaystyle {\lim_{\Delta x \rightarrow 0}} \frac{\frac {1}{(x+ \Delta x)^2} - \frac {1}{x^2}} {\Delta x}$

Should I get a common denominator in the top of the problem?

2. Originally Posted by yeloc
Use the definition of the derivative to find f' (x).

f (x)= $\displaystyle \frac {1}{x^2}$

f'(x)= $\displaystyle {\lim_{\Delta x \rightarrow 0}} \frac{\frac {1}{(x+ \Delta x)^2} - \frac {1}{x^2}} {\Delta x}$

Should I get a common denominator in the top of the problem?
yes. you should get a common denominator in the top, and simplify the top of numerator.

3. I got a common denominator of $\displaystyle x^4+2x^3 \Delta x+x^2 \Delta x^2$

So would the final answer be $\displaystyle \frac {-2x} {x^4}$ ?

4. Originally Posted by yeloc
I got a common denominator of $\displaystyle x^4+2x^3 \Delta x+x^2 \Delta x^2$

So would the final answer be $\displaystyle \frac {-2x} {x^4}$ ?
The answer is correct but can be simplified.

5. $\displaystyle \frac {-2} {x^3}$ I knew I missed something. Thanks!