Derivative Trig Help !!!

DancingQueen09

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Oct 24, 2009
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I look at this problem and I dont even know how to start... even worse complete it!!! If someone could please show me step by step how to get the answer to this problem I would greatly appreciate it : )

If
mathprob.jpg


Find f'(x) (the first derivative)

Thank you in advance <3<3<3
 
One little thing you could do is rewrite ln(1cos(x))=12ln(1cos(x))\displaystyle ln(\sqrt{1-cos(x)})=\frac{1}{2}ln(1-cos(x))

Use the chain rule. It is not as bad as it looks.

i.e. ddx[sin(ln(x))]=cos(ln(x))x\displaystyle \frac{d}{dx}[sin(ln(x))]=\frac{cos(ln(x))}{x}
 
f(x) = x2[sin(lnx)+cos(lnx)]+ln(1cosx)1/2, find f  (x).\displaystyle f(x) \ = \ \frac{x}{2}[sin(ln|x|)+cos(ln|x|)]+ln(1-cos|x|)^{1/2}, \ find \ f \ ' \ (x).

Now.instead of having a conniption fit or leaving for the nearest trauma center, break\displaystyle Now. instead \ of \ having \ a \ conniption \ fit \ or \ leaving \ for \ the \ nearest \ trauma \ center, \ break

the equation down to parts that are more manageable, to wit:\displaystyle the \ equation \ down \ to \ parts \ that \ are \ more \ manageable, \ to \ wit:

x2[sin(lnx)+cos(lnx)]+12ln(1cosx)\displaystyle \frac{x}{2}[sin(ln|x|)+cos(ln|x|)]+\frac{1}{2}ln(1-cos|x|)

= 12[xsin(lnx)+xcos(lnx)+ln(1cosx)].\displaystyle = \ \frac{1}{2}[xsin(ln|x|)+xcos(ln|x|)+ln(1-cos|x|)].

= 12[(1)sin(lnx)+xcos(lnx)x+(1)cos(lnx)xsin(lnx)x+sin(x)1cos(x)]\displaystyle = \ \frac{1}{2}\bigg[(1)sin(ln|x|)+\frac{xcos(ln|x|)}{x}+(1)cos(ln|x|)-\frac{xsin(ln|x|)}{x}+\frac{sin(x)}{1-cos(x)}\bigg]

= 12[sin(lnx)+cos(lnx)+cos(lnx)sin(lnx)+sin(x)1cos(x)]\displaystyle = \ \frac{1}{2}\bigg[sin(ln|x|)+cos(ln|x|)+cos(ln|x|)-sin(ln|x|)+\frac{sin(x)}{1-cos(x)}\bigg]

= cos(lnx)+(12)sin(x)1cos(x) QED\displaystyle = \ cos(ln|x|)+\bigg(\frac{1}{2}\bigg)\frac{sin(x)}{1-cos(x)} \ QED

Now, all in all, that wasnt so bad, now was it.\displaystyle Now, \ all \ in \ all, \ that \ wasn't \ so \ bad, \ now \ was \ it.
 
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