## bigcat Group Title find the derivative of f(x)=x^2 + x -3 using the definition of the derivative one year ago one year ago

1. Callisto Group Title

$f'(x)$$=\lim_{h \rightarrow 0}\frac{f(x+h) - f(x)}{h}$$=\lim_{h \rightarrow 0}\frac{[(x+h)^2 + (x+h) -3] -(x^2 + x -3)}{h}$Can you simplify the fraction first?

2. bigcat Group Title

I used x^2 + 2(x)(h) + h^2 + x +h -3 -x^2 -x +3 = 2x + x ??

3. Callisto Group Title

x^2 + 2(x)(h) + h^2 + x +h -3 -x^2 -x +3 <- correct for denominator. But it's not equal to 2x + x... $x^2 + 2(x)(h) + h^2 + x +h -3 -x^2 -x +3$Group the like terms together: $x^2 -x^2 + x -x -3 +3+ h^2+ 2(x)(h)+h$ Now, can you simplify the above expression

4. bigcat Group Title

basically factor out the h and H(h+2x+1) divided by the h on denominator and = h + 2x + 1?

5. Callisto Group Title

Yes.

6. Callisto Group Title

And you got: $\lim_{h \rightarrow 0} (h+2x+1)$Can you evaluate the limit?

7. bigcat Group Title

Would be 2x + 1 ??? Because h is going to 0

8. Callisto Group Title

Indeed it is!

9. bigcat Group Title

Holy Cow! It came together finally!! Thank you very much for your help! I would have been stuck!!!

10. Callisto Group Title

You're welcome :)

11. bigcat Group Title

Have a great day!!

12. Callisto Group Title

You too! :)