# Thread: A little derivative help (definition of derv.)

1. ## A little derivative help (definition of derv.)

Hey guys, I'm using the definition of derivative to find f'(a), this always makes a mess. This is what I have done so far;

Question: f(t) = 2t3+t, find f'(a).

So,

lim f(a+h)-f(a)/(h) - the formula
h->0

lim 2(a+h)+(a+h)-(2(a)3+a)/(h)
h->0

Here's all the foiling etc I did on the side:

(a+h)(a+h)(a+h)
(a2+2ah+h2)(a+h)
eventually getting....2(a3+3a2h+3ah2+h3) = 2a3+6a2h+6ah2+2h3

so now I have,

lim 2a3+6a2h+6ah2+2h3+a-h-2a3-a/(h)
h->0

lim 6a2​h+6ah2+2h3-h/(h)
h->0

lim 6a2h+6ah2+2h3
h->0

6a2(0)+6a(0)2+2(0)3-1 = -1

f'(a) = -1?

Not sure where I went wrong, the derivative of 2t3​+t is definitely not -1. Could use some guidance.

Thank you.

Ok so I figured out that I missed a step, after

lim 6a2h+6ah2+2h3-h/(h)
h->0

I should have isolated h so I get

lim h(6a2+6ah+2h2-1)/h (now cancel out the h's)
h->0

lim 6a2-6ah-2h2+1
h->0

6a2-0-0+1

= 6a2​+1 how does this look?

Looks good!

3. ## Re: A little derivative help (definition of derv.)

Originally Posted by MarkFL
Looks good!
Lol thanks, these question are a pain in the butt >.<