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ERoseM Group Title

Find f prime (x) if f(x) = (cosx)/(1+secx)

  • 2 years ago
  • 2 years ago

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  1. lgbasallote Group Title
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    have you tried quotient rule?

    • 2 years ago
  2. ERoseM Group Title
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    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

    • 2 years ago
  3. calculusfunctions Group Title
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    Show us how far you got with the quotient rule. Show all the steps you have so far. Can you do that?

    • 2 years ago
  4. ERoseM Group Title
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    Yes, I get (|dw:1350172024457:dw|

    • 2 years ago
  5. calculusfunctions Group Title
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    Correct! So far! Now what do you think the next step should be to simplify?

    • 2 years ago
  6. calculusfunctions Group Title
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    You're only going to simplify the numerator. Never expand the denominator. Do you understand?

    • 2 years ago
  7. ERoseM Group Title
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    Yes. Should I distribute the -sinx to (1+secx)?

    • 2 years ago
  8. calculusfunctions Group Title
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    Go ahead and apply the distributive property to the numerator. In other words, expand.

    • 2 years ago
  9. calculusfunctions Group Title
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    Yes! Go ahead. Show me the next step.

    • 2 years ago
  10. ERoseM Group Title
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    |dw:1350172306983:dw| I shouldn't distribute the cosx correct? Because tanx and secx are being multiplied together?

    • 2 years ago
  11. calculusfunctions Group Title
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    Yes expand the entire numerator. Meaning I shouldn't see any more parentheses in the numerator. Go ahead!

    • 2 years ago
  12. calculusfunctions Group Title
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    After that change each sec x to 1/cos x. Understood? Go ahead.

    • 2 years ago
  13. calculusfunctions Group Title
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    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?

    • 2 years ago
  14. ERoseM Group Title
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    Yes. I am just confused on what I should do to the -cosx(tanxsecx)

    • 2 years ago
  15. calculusfunctions Group Title
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    \[-\cos x(\tan x \sec x)=-(\cos x)(\tan x)(\frac{ 1 }{ \cos x })\]Agreed?

    • 2 years ago
  16. calculusfunctions Group Title
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    So do exactly that. Go ahead.

    • 2 years ago
  17. calculusfunctions Group Title
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    Now show me the step in it's entirety.

    • 2 years ago
  18. ERoseM Group Title
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    Okay.

    • 2 years ago
  19. ERoseM Group Title
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    |dw:1350172978272:dw|

    • 2 years ago
  20. calculusfunctions Group Title
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    \[f \prime(x)=\frac{ -\sin x(1+\sec x)-\cos x(\sec x \tan x) }{(1+\sec x)^{2} }\] \[f \prime(x)=\frac{ -\sin x -\sin x \sec x -\cos x \sec x \tan x }{ (1+\sec x)^{2} }\] \[f \prime(x)=\frac{ -\sin x -\sin x(\frac{ 1 }{ \cos x })-\cos x(\frac{ 1 }{ \cos x })\tan x }{ (1+\sec x)^{2} }\] 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.

    • 2 years ago
  21. calculusfunctions Group Title
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    You are correct in that you should change the sin x/cosx to tan x. Go ahead and show me the next step.

    • 2 years ago
  22. ERoseM Group Title
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    Can you multiply sinx and put it over cosx to get tangent on the left too?

    • 2 years ago
  23. calculusfunctions Group Title
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    Of course!\[\sin x(\frac{ 1 }{ \cos x })=\frac{ \sin x }{ \cos x }=\tan x\]

    • 2 years ago
  24. ERoseM Group Title
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    |dw:1350174177943:dw|

    • 2 years ago
  25. calculusfunctions Group Title
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    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!

    • 2 years ago
  26. calculusfunctions Group Title
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    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.

    • 2 years ago
  27. ERoseM Group Title
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    |dw:1350174369510:dw| Thank you for all your help

    • 2 years ago
  28. calculusfunctions Group Title
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    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.

    • 2 years ago
  29. calculusfunctions Group Title
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    The simplified answer should be\[f \prime(x)=\frac{ -\sin x -2\tan x }{ (1+\sec x)^{2} }\]

    • 2 years ago
  30. ERoseM Group Title
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    |dw:1350174836525:dw|

    • 2 years ago
  31. calculusfunctions Group Title
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    So you understand where you went wrong?

    • 2 years ago
  32. calculusfunctions Group Title
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    Do you understand how to do this now?

    • 2 years ago
  33. ERoseM Group Title
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    Yes, I think so, its just such a long process that I feel like I make mistakes so easily.

    • 2 years ago
  34. ERoseM Group Title
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    Thank you so much for your help, thanks for following the process with me!

    • 2 years ago
  35. calculusfunctions Group Title
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    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.

    • 2 years ago
  36. calculusfunctions Group Title
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    My pleasure. If you'd like any more help, let me know.

    • 2 years ago
  37. ERoseM Group Title
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    Thank you so much!!

    • 2 years ago
  38. calculusfunctions Group Title
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    Welcome anytime!

    • 2 years ago
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