# Thread: Finding the Derivative by Limit Process

1. ## Finding the Derivative by Limit Process

I have the function:
$\displaystyle f(x)=5x+6$

I need to "find the derivative by the limit process".

Using:
$\displaystyle (f(x+deltax)-f(x))/deltax$

My work:
$\displaystyle (5(x+deltax)+6-(5x+6))/deltax$

$\displaystyle (5x+5deltax+6-(5x+6))/deltax$

The two 5x's go away, the 5Δx and Δx go away, so I'm left with 12, which isn't the answer.

I'm lost.

2. $\displaystyle =\lim_{h\to 0 }\frac{f(x+h)-f(x)}{h}$

$\displaystyle =\lim_{h\to 0 }\frac{5(x+h)+6-(5x+6)}{h}$

$\displaystyle =\lim_{h\to 0 }\frac{5x+5h+6-5x-6}{h}$

$\displaystyle =\lim_{h\to 0 }\frac{5h}{h}$

$\displaystyle =\lim_{h\to 0 }5$

$\displaystyle =5$

3. Thanks a lot. I need to start using $\displaystyle h$ instead of Δx, since Δx is pretty confusing.

4. I agree with this.

5. New question...

There's just way too many things on my paper and I'm just lost now .

6. This one will take some doing, here's the first bit, now gettting expanding!

$\displaystyle =\lim_{h\to 0 }\frac{\left(9(x+h)^2-3(x+h)-\frac{3}{(x+h)^2}\right)-\left(9x^2-3x-\frac{3}{x^2}\right)}{h}$