How do you differentiate g(x) = [1 + sin(2x)]/[1 - sin(2x)] using the product rule?
1 Answer
Jan 9, 2016
In order to forcedly use the product rule, we'll rewrite it as
Explanation:
Also, we'll need chain rule to differentiate the second term.
-
Chain rule:
(dy)/(dx)=(dy)/(du)(du)/(dv)(dv)/(dx) -
For the first term, we'll rename
u=2x -
For the second term, we'll rename
v=(1-sin(w)) andw=2x (but the logic follows the same way that ofu ,v , and so on) -
Product rule:
(ab)'=a'b+ab'
Substituting