Derivative of f(x) = 7/(3x^3) and separate derivative of g(x) = 3/(x+7...

Question

anonymous · Answer

$$f \prime(x) = 7\times(-3)/3x ^{4} = -7/x ^{4}$$
$$g \prime(x) = -3/(x+7)^{2}$$

agreene · Answer

$$\frac{d}{dx} (\frac{7}{3x^3})$$
start by factoring out the constants.
$$\frac{7}{3}(\frac{d}{dx}(\frac1{x^3}))$$
x^-3 derives to -3/(4x^4)
combine that with our fraction out front and you should find:
$$- \frac{7}{x^4}$$

agreene · Answer

once you clarify what your g(x) is, we'll know what you're asking, lol.

anonymous · Answer

g(x) is a seperate problem. g(x) = 3/(x+7)

agreene · Answer

I would start by factoring the 3 out and then chain rule the resulting fraction. suyash011's answer seems correct to me.

anonymous · Answer

If I was asked to use the definition of derivative to find the solution, does that change the answer?

agreene · Answer

That wouldn't change the answer, but it would change the way you got it. You'll need to use the limit notation (which you will soon never need again).

agreene · Answer

$$f'(x)=\lim_{h\rightarrow 0}\frac{f(a+h)-f(a)}{h}$$
If I'm remembering it correctly.

anonymous · Answer

yah that's it. The system I'm required to enter the answers into say the answer to g(x) is correct, but the answer to f(x) isn't... is it possible that the answer is something else? Thanks for all your help by the way..

agreene · Answer

well, by definition there shouldnt be any difference--let me try and do the long way (with the limit) and see if I get something different somehow.

agreene · Answer

Well--that limit seems to go to 1. http://www.wolframalpha.com/input/?i=lim+h-%3E0+%28%28%283%2F%28x%2B7%29+%2Bh%29-%283%2F%28x%2B7%29%29%29%2Fh+%29

anonymous · Answer

I see that you have given us two derivatives...but have not defined the question....

anonymous · Answer

What are you being asked to find?

anonymous · Answer

PROSS, I'm asked to find the derivative of f(x) = 7/(3x^3).

anonymous · Answer

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