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

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

dumbcow
 2 years ago
Best ResponseYou've already chosen the best response.1ok 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

dumbcow
 2 years ago
Best ResponseYou've already chosen the best response.1let 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 \[\rightarrow \frac{215x^{4}}{2\sqrt{2x3x^{5}}}\]

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

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

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