Old 11-15-2006, 04:37 PM   #1
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Default Calculus

This problem was from my daily test today in calculus. Even after seeing it worked out, I still don't quite understand it >.>

Here's the problem:
f(x) = (g(x))^5
g(2) = -1
f '(2) = 5
g '(2 = ?

Hopefully someone on here can help me to understand it =/
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Old 11-15-2006, 04:40 PM   #2
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Default Re: Calculus

i forgot the rules i learned in calculus otherwise that problem doesnt really look so hard, i could have probabli done it in a flash if i were still in my old class.
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Old 11-15-2006, 04:48 PM   #3
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Default Re: Calculus

Im probably forgetting something extremely simple to this problem, but I just can't understand how to work it out >.>

50 credits says I feel retarded for not knowing how to do the problem
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Old 11-15-2006, 04:51 PM   #4
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Default Re: Calculus

Well, f'(x) = 5(g(x))^4*g'(x), right? So, 5(-1)^4*5=25

Edit: I think I answered the wrong question.

g'(2)=5

Edit2: What have I done? I don't even remember how I came up with g'(2)=5 in that first part.

Edit3: Okay, I think I fixed it now. f'(x) = 5(g(x))^4*g'(x) so 5=5(g'(2))^4, so 1=(g'(2))^4, so g'(2)=1
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Old 11-15-2006, 04:54 PM   #5
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Default Re: Calculus

Thanks for your astounding help, thyrax.

First, differentiate the given expression (make note of the chain rule)

f'(x) = [5(g(x))^4]g'(x)

Then just substitute in your values for x = 2

f'(2) = [5(g(2))^4]g'(2)

5 = [5(-1)^4]g'(2)

5 = 5(1)g'(2)

g'(2) = 1

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Old 11-15-2006, 04:57 PM   #6
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Default Re: Calculus

Guido's way also works.
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Old 11-15-2006, 05:01 PM   #7
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Default Re: Calculus

Haha, wow, I realized I was forgetting something extremely simple >.> I failed to realize all I had to do, after the chain rule, was simply substitute in a 2 for each x value.

Thanks Guido for the work, and Doug31 for at least trying =D
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Old 11-15-2006, 05:04 PM   #8
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Default Re: Calculus

I fixed it so that my way works now, before I saw guido's answer.
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Old 11-15-2006, 05:13 PM   #9
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Default Re: Calculus

Actually Doug, your way allows for 1 and -1 to be answers =P
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Old 11-15-2006, 05:15 PM   #10
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Default Re: Calculus

I know, I often get answers that are negative that I know should be positive, but then I just get rid of the negative sign.
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