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

1 Answer
Jun 19, 2016

(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)