A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 4 years ago
find dy/dx for sqrt of (9+ ((x9)/6)^1/5) ?
i don't know how to do this...
anonymous
 4 years ago
find dy/dx for sqrt of (9+ ((x9)/6)^1/5) ? i don't know how to do this...

This Question is Closed

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I think nesting of differentiation is a good idea.. \[\huge \frac{ d }{ dx } (\sqrt{9+(\frac{ x9 }{ 6 })^{\frac{ 1 }{ 5 }}})\] \[\huge \frac{ d }{ dx } (x^{n+1}) = (n+1)x^{n}\] then use the chain rule \[\huge \sqrt{x} = x^{\frac{ 1 }{ 2}}\] hope this will assist you

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0i still did not get it.. can u teach me in detail?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I don't know I will be able to complete, thre is a chance of power failure here.. but let me try

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0ok... as a first we need to know chain rule of differentiation

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0as an example \[\huge \frac{ d }{ dx } (\sqrt{a+x^{n}}) = \frac{ d }{ dx } ({a+x^{n}})^\frac{ 1 }{ 2 }\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0a function of x... and find the derivative by function by function using the chain rule...(function by function differntiation)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0here first function is square root (raised to 1/2) second function of x is \[\large x^{n}\] chain rule states that \[\huge \frac{ d }{ dx }(f(g(x))) = f^{'}(g(x))\times g^{'}(x)\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0here in this example square root is f(x) and \[\large x^{n}\] is g(x) Hope that now you can some what understand

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0i think i get a little what do u say...

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0so the answer for the example becomes \[\huge (a+x^{n})^{\frac{ 1 }{ 2 }} \times (0+n \times x^{n1}) \] which is equal to \[\huge (a+x^{n})^{\frac{ 1 }{ 2 }} \times(n \times x^{n1}) \]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0hope you under stood... so comming back to your question can you say how many functions are there in your qustion?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0try to figure out what is the functions... and how you can apply chain rule.... and refer example when in doubt... i listd the needed formule in my first reply...(expect chain rule, which is listed in above comments)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0yes you are right... two functions... I think powerfailure will be happening in a minute :(

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0ok..then i try i get 1/2((9+(x9)/6)^1/5)^1/2 . 1/30((x9)/6)^4/5) its right or not?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0yes .. it is right......(sorry for late reply) glad you figured out
Ask your own question
Sign UpFind 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.