Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
roselin
Group Title
Find the derivative of the functionusing the chain rule. k(x)= x^2 sec(1/x)
 2 years ago
 2 years ago
roselin Group Title
Find the derivative of the functionusing the chain rule. k(x)= x^2 sec(1/x)
 2 years ago
 2 years ago

This Question is Closed

satellite73 Group TitleBest ResponseYou've already chosen the best response.0
need the product rule as well
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.0
start with \[2x\sec(\frac{1}{x})+x^2\frac{d}{dx}\sec(\frac{1}{x})\] second part requires chain rule
 2 years ago

roselin Group TitleBest ResponseYou've already chosen the best response.0
the one that you have done is by using the product rule?
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.0
the derivative of secant is secant tangent, and the derivative of \(\frac{1}{x}\) is \(\frac{1}{x^2}\)
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.0
so the whole thing is \[2x\sec(\frac{1}{x}+x^2\sec(\frac{1}{x})\tan(\frac{1}{x})\times (\frac{1}{x^2})\]
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.0
we can clean it up a bit as \[2x\sec(\frac{1}{x})\sec(\frac{1}{x})\tan(\frac{1}{x})\]
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.0
on account of the \(x^2\) cancel
 2 years ago

roselin Group TitleBest ResponseYou've already chosen the best response.0
If anytime i get a problem like this, do I have to use the product rule first and then continue with the chain rule?
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.0
well it is not really a matter of "what goes first" you have to use the rules as you need them \(x^2\sec(\frac{1}{x})\) is a product so you need the product rule for sure also \(\sec(\frac{1}{x})\) is a composite function, so you must use the chain rule when you take the derivative
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.0
just like if you have a quotient, you have to use the quotient rule, but if the numerator is a product, you will need the product rule for that one and if the denominator is a composite function you will need the chain rule for it use whatever rules you need to get the derivative
 2 years ago

roselin Group TitleBest ResponseYou've already chosen the best response.0
i have one more question/problem.would you be willing to help me out ?
 2 years ago
See more questions >>>
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.