anonymous
  • anonymous
Find the derivative of the function-using the chain rule. k(x)= x^2 sec(1/x)
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
need the product rule as well
anonymous
  • anonymous
start with \[2x\sec(\frac{1}{x})+x^2\frac{d}{dx}\sec(\frac{1}{x})\] second part requires chain rule
anonymous
  • anonymous
okay

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
the one that you have done is by using the product rule?
anonymous
  • anonymous
the derivative of secant is secant tangent, and the derivative of \(\frac{1}{x}\) is \(-\frac{1}{x^2}\)
anonymous
  • anonymous
yes
anonymous
  • anonymous
okay,
anonymous
  • anonymous
so the whole thing is \[2x\sec(\frac{1}{x}+x^2\sec(\frac{1}{x})\tan(\frac{1}{x})\times (-\frac{1}{x^2})\]
anonymous
  • anonymous
we can clean it up a bit as \[2x\sec(\frac{1}{x})-\sec(\frac{1}{x})\tan(\frac{1}{x})\]
anonymous
  • anonymous
on account of the \(x^2\) cancel
anonymous
  • anonymous
okay,
anonymous
  • anonymous
If anytime i get a problem like this, do I have to use the product rule first and then continue with the chain rule?
anonymous
  • anonymous
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
anonymous
  • anonymous
oh okay
anonymous
  • anonymous
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
anonymous
  • anonymous
i have one more question/problem.would you be willing to help me out ?

Looking for something else?

Not the answer you are looking for? Search for more explanations.