Question

FInd f'(a) for the function, f(x)=(1+2x)/(1+x)

lim h->0 ][(1+2(a+h))/(1+a+h)]-[(1+2a)/(1+a)]]/h

I got rid of the denominator

lim h->0 [(1+2a+2h)(1+a+h)]-[(1+2a)(1+a)]/h =4a+2

What's wrong with this? Should I multiply the denominators with h as well?

Answer 1

"lim h->0 [(1+2a+2h)(1+a+h)]-[(1+2a)(1+a)]/h =4a+2 "
Shouldn't it be
{[(1+2a+2h)(1+a)-(1+2a)(1+a+h)]/[(1+a+h)(1+a)]}/h
={[h]/[(1+a+h)(1+a)]}/h
=1/(1+a+h)(1+a)
I'm sure you can do the rest.

Answer 2

I got it, thanks :)

Answer 3

Great!