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

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Answer 1 · 2016-07-24T03:59:54

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

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

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

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

How do you differentiate f(x)=cot5x * cot3xf(x)=cot5x * cot3x using the product rule?