Question

Question #50154

Answer 1

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!