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

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

dumbcowBest 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
 one year ago

dumbcowBest ResponseYou've already chosen the best response.1
\[(215x^{4})\frac{1}{2}(2x5x^{3})^{1/2}\]
 one year ago

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

dumbcowBest ResponseYou've already chosen the best response.1
?? yes that is original function right
 one year ago

IsTimBest ResponseYou've already chosen the best response.0
No, the answer. Well, the first half that isn't dy/dx.
 one year ago

dumbcowBest ResponseYou've already chosen the best response.1
oh yeah...sqrt is same as exponent of 1/2
 one year ago

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

IsTimBest ResponseYou've already chosen the best response.0
Also, why is their exponent positive, but ours is negative?
 one year ago

dumbcowBest 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
 one year ago

IsTimBest 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.
 one year ago

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

dumbcowBest 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
 one year ago

IsTimBest ResponseYou've already chosen the best response.0
Oh no! How do I do the first part?
 one year ago

dumbcowBest ResponseYou've already chosen the best response.1
sqrt is same as exponent of 1/2
 one year ago

IsTimBest ResponseYou've already chosen the best response.0
I guess I can't copy Latex....
 one year ago

IsTimBest ResponseYou've already chosen the best response.0
dy/dx=(2=15x^4)/(2sqrt(2x−3x^5))
 one year ago

IsTimBest ResponseYou've already chosen the best response.0
How do I figure that out?
 one year ago

dumbcowBest 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 \[\rightarrow \frac{215x^{4}}{2\sqrt{2x3x^{5}}}\]
 one year ago

IsTimBest ResponseYou've already chosen the best response.0
How'd you get du = 215x^4?
 one year ago

IsTimBest ResponseYou've already chosen the best response.0
@dumbcow When you have time...
 one year ago

dumbcowBest 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 \[\large \frac{d}{dx} x^{n} = n*x^{n1}\]
 one year ago
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