How do you differentiate # f(x)=cot(x)cos(x)# using the product rule?

1 Answer
Oct 28, 2015

Answer:

This is more a pointer in the correct direction:

Explanation:

Once you know that #d/dx(cot(x)) = -1-cot^2(x)#

and you combine it with #d/dx (uv) = v(du)/dx + u(dv)/dx#

You are off to a flying start. Just substitute and play until you find a solution:

As a check I put it into Maple which gave: #(-1 -cot^2{x})cos(x) -cot(x)sin(x)#

Maple outputs are sometimes a little 'Maple'ish' so need to be translated.

remember that #cot(x) = 1/(tan(x)) = (cos(x))/(sin(x))#
so you may be able to use:

#-cos(x)-(cos^3(x))/( sin^2(x)) - (cos(x)sin(x))/(sin(x))#