Question

How do you differentiate `f(x)=sin2x * cotx` using the product rule?

Answer 1

`2cos2x*cotx-csc^2x*sin2x`

Explanation:

• The product rule:
  `d/(dx)[f(x)]=("derivative of the first term" * "the second term")+("derivative of the second term"*"the first term")`

• `d/dx[cotx]=-csc^2x`

• `d/(dx)[f(x)]= (d/dx[sin(2x)]*cotx)+(d/dx[cotx]*sin2x)`
  `=(2cos2x*cotx)+(-csc^2x*sin2x)`
  `=2cos2x*cotx-csc^2x*sin2x`

• You could just stop there, or you could simplify the answer further by uniting all the angles as `x` using double angle formulas.