Question

Find the derivative of f(a)=(2a+1)/(a+3) at a using the definition of a derivative

Answer 1

I know the definition is lim h->0 (f(x+h)-f(x))/h, i'm just getting stuck with all of the algebra simplifying

Answer 2

Sure, show me how far you can get with the simplifying and I'll see what I can do to help you finish it. That way I can tell you only the important things you want to learn and not repeat stuff you already know, ya know? haha

Answer 3

Here's my work so far:

Answer 4

I keep ending up with 5/(a+3) but the answer is 5/(a+3)^2

Answer 5

Are you familiar with the Quotient Rule?

Answer 6

^not applicable since he/she needs to use limit definition to find answer.

Answer 7

Yup i don't think i've learned Quotient rule yet... this is only Ch. 2

Answer 8

a^2+6a+9=(a+3)^2

Answer 9

for denominator.

Answer 10

I see

Answer 11

@OOOPS yep i got that, but then taking the limit that goes to 0, right?

Answer 12

nope, the second term -->0 when taking limit, so, you just have 5/(a+3)^2

Answer 13

It looks like you have the correct answer so far through all your work, you even have (a+3)^2 written!

Maybe you need to just rewrite your fractions more carefully? On the second page you have: \[\LARGE \frac{(\frac{5h}{a^2+6a+9+3h+ah})}{h}\] which simplifies to: \[\Large \frac{5h}{h(a^2+6a+9+3h+ah)}= \frac{5}{a^2+6a+9+3h+ah}\]