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IsTim
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Express each function as a power with a rational exponent, and then differentiate. Express each answer using positive exponents. y=sqrt(2x3x^5)
 2 years ago
 2 years ago
IsTim Group Title
Express each function as a power with a rational exponent, and then differentiate. Express each answer using positive exponents. y=sqrt(2x3x^5)
 2 years ago
 2 years ago

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IsTim Group TitleBest ResponseYou've already chosen the best response.0
Well. I'm just doing the first part. I got 1/2(215x^4)^1/2
 2 years ago

dumbcow Group TitleBest ResponseYou've already chosen the best response.1
ok sqrt is same as exponent of 1/2 then apply chain rule to differentiate good..wait don't change inside...multiply whole thing by derivative of inside
 2 years ago

dumbcow Group TitleBest ResponseYou've already chosen the best response.1
\[(215x^{4})\frac{1}{2}(2x5x^{3})^{1/2}\]
 2 years ago

dumbcow Group TitleBest ResponseYou've already chosen the best response.1
**typo 3x^5
 2 years ago

IsTim Group TitleBest ResponseYou've already chosen the best response.0
In my textbook, it says: \[y=(2x3x^5)^{1/2}\]
 2 years ago

dumbcow Group TitleBest ResponseYou've already chosen the best response.1
?? yes that is original function right
 2 years ago

IsTim Group TitleBest ResponseYou've already chosen the best response.0
No, the answer. Well, the first half that isn't dy/dx.
 2 years ago

dumbcow Group TitleBest ResponseYou've already chosen the best response.1
oh yeah...sqrt is same as exponent of 1/2
 2 years ago

IsTim Group TitleBest ResponseYou've already chosen the best response.0
But I don't know how to get \[dy/dx=(2=15x^4 )/(2\sqrt{2x3x^5}\]
 2 years ago

IsTim Group TitleBest ResponseYou've already chosen the best response.0
Also, why is their exponent positive, but ours is negative?
 2 years ago

dumbcow Group TitleBest ResponseYou've already chosen the best response.1
same answer i posted....ours is negative because its in numerator, when you flip it to denominator the sign of exponent changes
 2 years ago

IsTim Group TitleBest ResponseYou've already chosen the best response.0
Ok. I understand the first part. Thanks. I'll call out if I need help on the second part.
 2 years ago

IsTim Group TitleBest ResponseYou've already chosen the best response.0
Um, to find the derviative I use 1/2(2x−5x^3)−1/2 right.
 2 years ago

dumbcow Group TitleBest ResponseYou've already chosen the best response.1
whoah ...um we were doing 2nd part (finding derivative this whole time) or at least thats what i was doing
 2 years ago

IsTim Group TitleBest ResponseYou've already chosen the best response.0
Oh no! How do I do the first part?
 2 years ago

dumbcow Group TitleBest ResponseYou've already chosen the best response.1
sqrt is same as exponent of 1/2
 2 years ago

IsTim Group TitleBest ResponseYou've already chosen the best response.0
To get dy/dx=(2=15x^4)
 2 years ago

IsTim Group TitleBest ResponseYou've already chosen the best response.0
/(22x−3x5−−−−−−−√
 2 years ago

IsTim Group TitleBest ResponseYou've already chosen the best response.0
I guess I can't copy Latex....
 2 years ago

IsTim Group TitleBest ResponseYou've already chosen the best response.0
dy/dx=(2=15x^4)/(2sqrt(2x−3x^5))
 2 years ago

IsTim Group TitleBest ResponseYou've already chosen the best response.0
How do I figure that out?
 2 years ago

dumbcow Group TitleBest ResponseYou've already chosen the best response.1
let me try this, part 1 is super easy all you are doing is rewriting it using rational exponents \[\large \sqrt[n]{x} = x^{1/n}\] \[\sqrt{2x3x^{5}} = (2x3x^{5})^{1/2}\] part 2: find derivative using chain rule u = 2x3x^5 du = 215x^4 \[\frac{d}{du} u^{1/2} = \frac{1}{2}u^{1/2} = \frac{1}{2\sqrt{u}}\] multiply by du and substitute 2x3x^5 back in for u \[\rightarrow \frac{215x^{4}}{2\sqrt{2x3x^{5}}}\]
 2 years ago

IsTim Group TitleBest ResponseYou've already chosen the best response.0
How'd you get du = 215x^4?
 2 years ago

IsTim Group TitleBest ResponseYou've already chosen the best response.0
@dumbcow When you have time...
 2 years ago

dumbcow Group TitleBest ResponseYou've already chosen the best response.1
isn't that what you got in your very 1st post ^^ ?? anyway, its the derivative of 2x3x^5 using power rule \[\large \frac{d}{dx} x^{n} = n*x^{n1}\]
 2 years ago
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