## ERoseM Group Title Find f prime (x) if f(x) = (cosx)/(1+secx) one year ago one year ago

1. lgbasallote Group Title

have you tried quotient rule?

2. ERoseM Group Title

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

3. calculusfunctions Group Title

Show us how far you got with the quotient rule. Show all the steps you have so far. Can you do that?

4. ERoseM Group Title

Yes, I get (|dw:1350172024457:dw|

5. calculusfunctions Group Title

Correct! So far! Now what do you think the next step should be to simplify?

6. calculusfunctions Group Title

You're only going to simplify the numerator. Never expand the denominator. Do you understand?

7. ERoseM Group Title

Yes. Should I distribute the -sinx to (1+secx)?

8. calculusfunctions Group Title

Go ahead and apply the distributive property to the numerator. In other words, expand.

9. calculusfunctions Group Title

Yes! Go ahead. Show me the next step.

10. ERoseM Group Title

|dw:1350172306983:dw| I shouldn't distribute the cosx correct? Because tanx and secx are being multiplied together?

11. calculusfunctions Group Title

Yes expand the entire numerator. Meaning I shouldn't see any more parentheses in the numerator. Go ahead!

12. calculusfunctions Group Title

After that change each sec x to 1/cos x. Understood? Go ahead.

13. calculusfunctions Group Title

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?

14. ERoseM Group Title

Yes. I am just confused on what I should do to the -cosx(tanxsecx)

15. calculusfunctions Group Title

$-\cos x(\tan x \sec x)=-(\cos x)(\tan x)(\frac{ 1 }{ \cos x })$Agreed?

16. calculusfunctions Group Title

So do exactly that. Go ahead.

17. calculusfunctions Group Title

Now show me the step in it's entirety.

18. ERoseM Group Title

Okay.

19. ERoseM Group Title

|dw:1350172978272:dw|

20. calculusfunctions Group Title

$f \prime(x)=\frac{ -\sin x(1+\sec x)-\cos x(\sec x \tan x) }{(1+\sec x)^{2} }$ $f \prime(x)=\frac{ -\sin x -\sin x \sec x -\cos x \sec x \tan x }{ (1+\sec x)^{2} }$ $f \prime(x)=\frac{ -\sin x -\sin x(\frac{ 1 }{ \cos x })-\cos x(\frac{ 1 }{ \cos x })\tan x }{ (1+\sec x)^{2} }$ 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.

21. calculusfunctions Group Title

You are correct in that you should change the sin x/cosx to tan x. Go ahead and show me the next step.

22. ERoseM Group Title

Can you multiply sinx and put it over cosx to get tangent on the left too?

23. calculusfunctions Group Title

Of course!$\sin x(\frac{ 1 }{ \cos x })=\frac{ \sin x }{ \cos x }=\tan x$

24. ERoseM Group Title

|dw:1350174177943:dw|

25. calculusfunctions Group Title

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!

26. calculusfunctions Group Title

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.

27. ERoseM Group Title

|dw:1350174369510:dw| Thank you for all your help

28. calculusfunctions Group Title

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.

29. calculusfunctions Group Title

The simplified answer should be$f \prime(x)=\frac{ -\sin x -2\tan x }{ (1+\sec x)^{2} }$

30. ERoseM Group Title

|dw:1350174836525:dw|

31. calculusfunctions Group Title

So you understand where you went wrong?

32. calculusfunctions Group Title

Do you understand how to do this now?

33. ERoseM Group Title

Yes, I think so, its just such a long process that I feel like I make mistakes so easily.

34. ERoseM Group Title

Thank you so much for your help, thanks for following the process with me!

35. calculusfunctions Group Title

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.

36. calculusfunctions Group Title

My pleasure. If you'd like any more help, let me know.

37. ERoseM Group Title

Thank you so much!!

38. calculusfunctions Group Title

Welcome anytime!