Question #50154

1 Answer
Nov 10, 2016

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!