Question

How do you differentiate `f(x)=ln2x * cot(5-x)` using the product rule?

Answer 1

`(df)/(dx)=cot(5-x)/x+csc^2(5-x)ln(2x)`

Explanation:

Product rule states if `f(x)=g(x)h(x)`

then `(df)/(dx)=(dg)/(dx)xxh(x)+(dh)/(dx)xxg(x)`

Hence as `f(x)=ln(2x)cot(5-x)`

`(df)/(dx)=1/(2x)xx2xxcot(5-x)-csc^2(5-x)xx(-1)xxln(2x)`

or `(df)/(dx)=cot(5-x)/x+csc^2(5-x)ln(2x)`