Freshman's Dream Quotient Rule

Question

I have been researching the Freshman's Dream Quotient Rule for awhile now and have been unable to find an example for which the rule works. I want to know if anyone knows of 2 function which it works for.

Rule is:

$$\left(\frac{f(x)}{g(x)}\right)'=\frac{f'(x)}{g'(x)}$$

Yes 0 and 1 would be the answers. So that one would not work. — user348202, Jun 27 '16 at 13:26
That is wrong, because one side would give me -4/x^2 and the other side would give me 0. — user348202, Jun 27 '16 at 13:28
Thanks, I just found it odd it does not hold. I thought maybe it was a mistake. — user348202, Jun 27 '16 at 13:33

score 2 · Answer 1 · answered Jun 27 '16 at 13:32

2

Define the functions $f$ and $g$ on $[1,+\infty]$.

$f(x)=0$ and $g(x)=x$, so $f'(x)=0$ and $g'(x)=1$.

$$\left(\frac{f(x)}{g(x)}\right)'=\left(\frac{0}{x}\right)'=0'=0$$

$$\frac{f(x)'}{g(x)'}=\frac{0}{1}=0$$

answered Jun 27 '16 at 13:32

Bérénice

9,367

Freshman's Dream Quotient Rule

1 Answers1