"Find f'(a) for f(x)=(1+2x)/(1+x)"

Question

I got 2, but the answer is 1/(1+a)^2.  How do I get that??

drwls · Answer

Differentiate f(x) to get f'(x), then
substitute a for x.

Let u = 1 + x
Then you want the derivative of (
(2u-1)/u. That is the derivative of -1/u (since the derivative of 2u/u is 0). The derivative is therefore is u^-2 = 1/(1+x)^2
That becomes 1/(1+a^2)when a is substituted for x.

Reiny · Answer

Did you get f'(x) = 2 by simply taking the derivative of the top over the derivative of the bottom ?? my oh my !!

Stuck · Answer

Thank you drwls! Reiny - yes I did! I only realized I did that after I posted my question. Wasn't thinking for a moment. ;)