Question #50154

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Answer 1 · 2016-11-10T14:23:19

Use a combination of the product and quotient rules.

Let $g(x) = xsinx$ .

$g'(x) = 1 xx sinx + x xx cosx = sinx + xcosx$

Let the entire function be $f(x) = (xsinx)/(1 + cosx)$ .

$f'(x) = ((sinx + xcosx)(1 + cosx) - (-sinx xx xsinx))/(1 + cosx)^2$

$f'(x) = (sinx + xcosx + sinxcosx + xcos^2x + xsin^2x)/(1 + cosx)^2$

$f'(x) = (sinx + xcosx + sinxcosx + x)/(1 + cosx)^2$

$f'(x) = (sinx(1 + cosx) + x(1 + cosx))/(1 + cosx)^2$

$f'(x) = ((sinx + x)(1 + cosx))/(1 + cosx)^2$

$f'(x) = ((sinx + x)(1 + cosx))/((1 + cosx)(1 + cosx))$

$f'(x) = (sinx + x)/(1 + cosx)$

Hopefully this helps!