mathcalculus
Derivative Question: Help (attached below)
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mathcalculus
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NoelGreco
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Get rid of the radicals.
anonymous
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hint:\[ x^5\sqrt{x}=x^{5+\frac{1}{2}}=x^{\frac{11}{2}}\]
mathcalculus
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right.. 3x^(11/2)
NoelGreco
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That's it, and go with a negative exponent on the second term to avoid the quotient rule.
mathcalculus
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+ -4*x^-7/2 ?
NoelGreco
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Yes.
mathcalculus
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i got: 3x^(11/2)+14/x^9/2..
mathcalculus
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@NoelGreco
NoelGreco
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\[3x ^{\frac{ 11 }{ 2 }}-4x ^{\frac{ -7 }{ 2 }}\]
Now take the derivative.
mathcalculus
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14x/x^9/2
mathcalculus
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?
NoelGreco
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The derivative of the second term is\[\frac{ d }{ dx }3x ^{\frac{ 11 }{ 2 }}=\frac{ 33 }{ 2 }x ^{\frac{ 9 }{ 2 }}\]
I don't know how you're trying to take the derivative, but you simply use the power rule on each term.
mathcalculus
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huh?
mathcalculus
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from 3x^ (11/2) + 14x^(-9/2)
mathcalculus
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doesn't the x9/2 down
mathcalculus
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@NoelGreco hey sorry to interrupt. but i just needed to figure this out before leaving..
anonymous
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\[\frac{d}{dx}14x^{-\frac{9}{2}}=-\frac{9}{2}\times 14x^{-\frac{9}{2}-1}\]whatever that is
mathcalculus
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this is my work so far:
sami-21
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Before applying the power rule combine the terms as told you previously .
\[\Large f(x)=3x^5.x^\frac{1}{2}-\frac{-4}{x^3.x^\frac{1}{2}}\]
combining the terms
\[\Large f(x)=3x^\frac{11}{2}-\frac{4}{x^\frac{7}{2}}\]
\[\Large f(x)=3x^\frac{11}{2}-4x^{-\frac{7}{2}}\]
now Apply the Power rule.
mathcalculus
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thank you are you still there @sami-21
mathcalculus
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i have one question if you dont mind
mathcalculus
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what if they ask: derivative of sqrt(6x)
mathcalculus
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i dont know why i always messed them up
mathcalculus
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i thought it would be like this:
= 6x^(1/2) then
=3x^(-1/2)
=3/(x^(1/2)
mathcalculus
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@sami-21
sami-21
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yes that is correct.