Question

How do you differentiate `f(x)=cot5x * cot3x` using the product rule?

Answer 1

`(df)/(dx)=-3cot5xcsc^2 3x-5cot3xcsc^2 5x`

Explanation:

According to product rule, if `f(x)=g(x)xxh(x)`

`(df)/(dx)=g(x)xx(dh)/(dx)+(dg)/(dx)xxh(x)`

Here as `g(x)=cot5x` and `h(x)=cot3x`, hence

`(df)/(dx)=cot5x xx-csc^2 3x xx3+(-csc^2 5x xx5xxcot3x)`

= `-3cot5xcsc^2 3x-5cot3xcsc^2 5x`