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What remains id to differentiate cos(2x). This involves use of the chain rule.
Hence I get
Penny Taiwo wrote back to penny, dear penny, thanks for the solution. i got the same answer but i was thinking maybe i was wrong. is that a first principle rule method of solving the problem y=xcos2x?. thank you Taiwo, If you are going to solve this from first principles you need to know
From first principles you want to evaluate the limit of [f(x + h)  f(x)]/h as h approaches 0 where f(x) = x cos(2x). Evaluating this expression and using the multiple angle expression for the cosine above I got I then multiplied through by (x + h) and collected terms to express the fraction above as the sum of three fractions Taking the limit of each of these fractions as h approaches zero I get
which agrees with the answer you and I both got using the product rule and the chain rule. Penny  


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