Two Ways to Solve

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Jason76

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Post Edited

\(\displaystyle f(x) = -\dfrac{12}{s^{4}}\)

\(\displaystyle f(x) = -12s^{-4}\)

\(\displaystyle f'(x) = (-4)12s^{-5}\)

\(\displaystyle f'(x) = -48s^{-5}\)

Another way to solve :confused:

\(\displaystyle f(x) = -\dfrac{12}{s^{4}}\)

\(\displaystyle f'(x) = \dfrac{[s^{4}][\dfrac{d}{ds} 12] - [12][\dfrac{d}{ds} s^{4}]}{(s^{4})^{2}}\) - using quotient rule: \(\displaystyle \dfrac{g(f') - f(g')}{g^{2}}\) given \(\displaystyle \dfrac{f}{g}\)

\(\displaystyle f'(x) = \dfrac{[s^{4}][0] - [12][4s^{3}]}{(s^{4})^{2}}\)

\(\displaystyle f'(x) = \dfrac{-48s^{3}}{s^{8}}\)

\(\displaystyle f'(x) = -48s^{-5}\)
 
Last edited:
Jason76 said:
\(\displaystyle f(x) = -\dfrac{12}{s^{4}}\)

\(\displaystyle f(x) = -12s^{-4}\)

\(\displaystyle f'(x) = -12x^{-3}\) ===> INCORRECT! f'(x) = 48s^(-5)

\(\displaystyle f'(x) = \dfrac{48}{s^{3}}\) ===> INCORRECT! f'(x) = 48/s^(5)



Another way to solve :confused:

\(\displaystyle f(x) = -\dfrac{12}{s^{4}}\)

\(\displaystyle f(x) = -12s^{-4}\) ===> Why are you doing this then you then apply the quotient rule in the next step?

\(\displaystyle f'(x) = \dfrac{[s^{4}][\dfrac{d}{dx} 12] - [12][\dfrac{d}{dx} s^{-4}]}{(s^{3})^{2}}\) ===> Errors embedded in this as well. Yes, you can use the quotient rule, but no need when you can do it the way you did it above by rewriting it with a negative exponent and then using the power rule.
Click to expand...
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d/dx \(\displaystyle ax^n = nax^{n-1}\) where a and n are constants. You have to know this basic rule as if it's born in you.

This problem is a case for the power rule. There aren't two factors that contain the variable s. There's no need to use product rule or quotient rule once you've rewritten as \(\displaystyle f(x) = -12s^{-4}\)

\(\displaystyle f'(x) = (-4)*(-12)s^{-4-1}= 48s^{-5} = \dfrac{48}{s^{5}}\)
 
Jason76 said:
Post Edited

\(\displaystyle f(x) = -\dfrac{12}{s^{4}}\)

\(\displaystyle f(x) = -12s^{-4}\)

\(\displaystyle f'(x) = (-4)12s^{-5}\)

\(\displaystyle f'(x) = -48s^{-5}\)

Another way to solve :confused:

\(\displaystyle f(x) = -\dfrac{12}{s^{4}}\)

\(\displaystyle f'(x) = \dfrac{[s^{4}][\dfrac{d}{ds} 12] - [12][\dfrac{d}{ds} s^{4}]}{(s^{4})^{2}}\) - using quotient rule: \(\displaystyle \dfrac{g(f') - f(g')}{g^{2}}\) given \(\displaystyle \dfrac{f}{g}\)

\(\displaystyle f'(x) = \dfrac{[s^{4}][0] - [12][4s^{3}]}{(s^{4})^{2}}\)

\(\displaystyle f'(x) = \dfrac{-48s^{3}}{s^{8}}\)

\(\displaystyle f'(x) = -48s^{-5}\)
Click to expand...

So what is the question??
 
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