A community for students.
Here's the question you clicked on:
 0 viewing
roselin
 2 years ago
Find the derivative of the functionusing the chain rule. k(x)= x^2 sec(1/x)
roselin
 2 years ago
Find the derivative of the functionusing the chain rule. k(x)= x^2 sec(1/x)

This Question is Closed

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

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

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

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

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

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

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

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

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0well 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

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0just 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

roselin
 2 years ago
Best ResponseYou've already chosen the best response.0i have one more question/problem.would you be willing to help me 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.