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Please Help! Clarifying the origins of a constant [Math C3 Trig Differentiation) watch

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    At 4 minutes in this video he used the rule (y=uv) >>> dy/dx = (u)(dv/dx) + (v)(du/dx).

    So when he differentiates tan(2y) why did it not end up as sec^2(2y)..
    Why did 2y then get differentiated and added on when it was already present in the first part?:

    [sec^2(2y)] [2]

    Surely it should be [sec^2(2y)], or [sec^2(2)] if he differentiates the 2y also but can someone please clarify why he used the 2y twice?

    Thanks.


    https://www.youtube.com/watch?v=DMwOe7AyqwM
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    I have not watched the video as I find them turgid however, probably

    this is because tan (2y) is a composite function where f(y) = tan(y) and g(y) = 2y fg(y)=tan (2y)

    Hence the differential (wrt y) is sec^2 (2y) multiplied by d/dy (2y) =2 >>> 2sec^(2y)

    This assumes that when you say 'added on' you were not talking mathematically but rather about the 2 multiplying.
    BTW, depending on what stage you are at you may be more comfortable treating the differentiation of tan(2y) as a case of using the chain rule.
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    Gotcha, that's sorted me out, thanks!
 
 
 
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