## anonymous 3 years ago find the derivative of f(x)=x^2 + x -3 using the definition of the derivative

1. Callisto

$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. anonymous

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

3. Callisto

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. anonymous

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

5. Callisto

Yes.

6. Callisto

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

7. anonymous

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

8. Callisto

Indeed it is!

9. anonymous

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

10. Callisto

You're welcome :)

11. anonymous

Have a great day!!

12. Callisto

You too! :)

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