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

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Answer 1 · 2016-06-19T06:57:18

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

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

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