anonymous
  • anonymous
Find f prime (x) if f(x) = (cosx)/(1+secx)
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.
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
lgbasallote
  • lgbasallote
have you tried quotient rule?
anonymous
  • anonymous
Yes, I did and then I don't know how to distribute? I know I have to use it It just doesn't fully come out
calculusfunctions
  • calculusfunctions
Show us how far you got with the quotient rule. Show all the steps you have so far. Can you do that?

Looking for something else?

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

More answers

anonymous
  • anonymous
Yes, I get (|dw:1350172024457:dw|
calculusfunctions
  • calculusfunctions
Correct! So far! Now what do you think the next step should be to simplify?
calculusfunctions
  • calculusfunctions
You're only going to simplify the numerator. Never expand the denominator. Do you understand?
anonymous
  • anonymous
Yes. Should I distribute the -sinx to (1+secx)?
calculusfunctions
  • calculusfunctions
Go ahead and apply the distributive property to the numerator. In other words, expand.
calculusfunctions
  • calculusfunctions
Yes! Go ahead. Show me the next step.
anonymous
  • anonymous
|dw:1350172306983:dw| I shouldn't distribute the cosx correct? Because tanx and secx are being multiplied together?
calculusfunctions
  • calculusfunctions
Yes expand the entire numerator. Meaning I shouldn't see any more parentheses in the numerator. Go ahead!
calculusfunctions
  • calculusfunctions
After that change each sec x to 1/cos x. Understood? Go ahead.
calculusfunctions
  • calculusfunctions
I mean change each sec x to 1/cos x only in the numerator. Never expand the denominator, like I said earlier. Do you understand?
anonymous
  • anonymous
Yes. I am just confused on what I should do to the -cosx(tanxsecx)
calculusfunctions
  • calculusfunctions
\[-\cos x(\tan x \sec x)=-(\cos x)(\tan x)(\frac{ 1 }{ \cos x })\]Agreed?
calculusfunctions
  • calculusfunctions
So do exactly that. Go ahead.
calculusfunctions
  • calculusfunctions
Now show me the step in it's entirety.
anonymous
  • anonymous
Okay.
anonymous
  • anonymous
|dw:1350172978272:dw|
calculusfunctions
  • calculusfunctions
\[f \prime(x)=\frac{ -\sin x(1+\sec x)-\cos x(\sec x \tan x) }{(1+\sec x)^{2} }\] \[f \prime(x)=\frac{ -\sin x -\sin x \sec x -\cos x \sec x \tan x }{ (1+\sec x)^{2} }\] \[f \prime(x)=\frac{ -\sin x -\sin x(\frac{ 1 }{ \cos x })-\cos x(\frac{ 1 }{ \cos x })\tan x }{ (1+\sec x)^{2} }\] Take a moment to look at this the first couple of steps are exactly what you did. Do you understand what I did in the third step and now first tell me what you think you should do.
calculusfunctions
  • calculusfunctions
You are correct in that you should change the sin x/cosx to tan x. Go ahead and show me the next step.
anonymous
  • anonymous
Can you multiply sinx and put it over cosx to get tangent on the left too?
calculusfunctions
  • calculusfunctions
Of course!\[\sin x(\frac{ 1 }{ \cos x })=\frac{ \sin x }{ \cos x }=\tan x\]
anonymous
  • anonymous
|dw:1350174177943:dw|
calculusfunctions
  • calculusfunctions
Have more confidence in yourself, would ya! You're doing just fine. Now continue with confidence. And even if you're wrong, so what? Being wrong is part of learning and part of life. So never be afraid to ask questions even if you think you're wrong. Now could you please show me the remaining steps, with confidence!
calculusfunctions
  • calculusfunctions
Not quite. There is an error in the numerator but it just seems to be a careless one. Retrace your steps to see if you can spot the error. Otherwise show me your previous step so that I can point it out to you.
anonymous
  • anonymous
|dw:1350174369510:dw| Thank you for all your help
calculusfunctions
  • calculusfunctions
No! Now look back carefully at the third step of the partial solution, I posted above. Is sin x multiplied by tan x? I don't think so.
calculusfunctions
  • calculusfunctions
The simplified answer should be\[f \prime(x)=\frac{ -\sin x -2\tan x }{ (1+\sec x)^{2} }\]
anonymous
  • anonymous
|dw:1350174836525:dw|
calculusfunctions
  • calculusfunctions
So you understand where you went wrong?
calculusfunctions
  • calculusfunctions
Do you understand how to do this now?
anonymous
  • anonymous
Yes, I think so, its just such a long process that I feel like I make mistakes so easily.
anonymous
  • anonymous
Thank you so much for your help, thanks for following the process with me!
calculusfunctions
  • calculusfunctions
By the way, if the question doesn't ask you to simplify then it is not wrong to even leave your derivative unsimplified. However every teacher is different so you may want to consult with yours. I prefer students to simplify to a certain degree unless I specifically ask not to simplify. But as I said every teacher is different.
calculusfunctions
  • calculusfunctions
My pleasure. If you'd like any more help, let me know.
anonymous
  • anonymous
Thank you so much!!
calculusfunctions
  • calculusfunctions
Welcome anytime!

Looking for something else?

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