A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing
 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)
 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)

This Question is Closed

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 \[\large \frac{d}{dx} x^{n} = n*x^{n1}\]
Ask your own question
Ask a QuestionFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.