Math Help - Chain Rule problem

1. Chain Rule problem

I'm supposed to apply the chain rule with the following question, and as far as I know, the chain rule is f '[g(x)] * g '(x).

According to the question, I need to find f[g(x)] and g[f(x)].

$f(x) = (x/8) + 7$ and $g(x) = 6x -1$

I thought I should simply just go as follows...

$(1/8)(6x -1) * 6$
= $(3/4)(6x - 1)$
$= (9x/2) - (3/4)$

This isn't the right answer, but I don't know what I'm doing wrong..

2. Re: Chain Rule problem

I'm confused as to what you are trying to do. Are you trying to simply find the composition or the derivative of the composition? Your post seems inconsistent on this.. can you state the whole question?

Perhaps the problem wants you to find f(g(x)) first, then the derivative of this composition, and see that the answer is the same if you use the chain rule?

3. Re: Chain Rule problem

Originally Posted by SworD
I'm confused as to what you are trying to do. Are you trying to simply find the composition or the derivative of the composition? Your post seems inconsistent on this.. can you state the whole question?

Perhaps the problem wants you to find f(g(x)) first, then the derivative of this composition, and see that the answer is the same if you use the chain rule?
I think you're on the right track..

The question from the text-book is as follows.

"Find f[g(x)] and g[f(x)].

f(x) = (x/8) + 7. g(x) = 6x - 1."

I really don't know what I should be doing with the question. The chapter it's from is on the chain rule, so I assumed I needed to use the chain rule to find the derivative of f[g(x)], but that doesn't seem to be the case.

If it helps at all, the answer I'm SUPPOSED to get is this...

(6x + 55)/8

4. Re: Chain Rule problem

Now that I've looked at the question properly, it doesn't seem to be asking me to find any derivatives.

Just f[(g(x)]. But I still don't know how I should be getting to the answer above.

I would have thought that f[g(x)] would equal...

[(6x - 1) / 8] + 7

?

5. Re: Chain Rule problem

It doesn't ask for derivatives. You just plug in g(x) into f(x) as though it were any number.

$f(g(x)) = \frac{(6x-1)}{8} + 7 = \frac{6x}{8} - \frac{1}{8} + \frac{56}{8} = \frac{6x + 55}{8}$

$g(f(x)) = 6\left (\frac{x}{8} + 7 \right) - 1 = \frac{6}{8}x + 42 - 1 = \frac{6}{8}x + 41$

Also, notice that if you take the derivative of either of these, you get $\frac{6}{8}$, consistent with the chain rule:

$f'(g(x) \cdot g'(x) = \frac{1}{8} \cdot 6 = \frac{6}{8}$

$g'(f(x) \cdot g'(x) = 6 \cdot \frac{1}{8} = \frac{6}{8}$

6. Re: Chain Rule problem

Thanks for that, I was just overthinking it all. Pretty self-explanatory in the end. I just forgot to look at 7 as a fraction instead of an integer...