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Math Help - Simplifying differential solutions - cotx e^4x

  1. #1
    Junior Member froodles01's Avatar
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    Simplifying differential solutions - cotx e^4x

    Question is f(x) = e^4x cotx
    Fine, I'll use product rule;
    dy/dx = V du/dx * U dv/dx
    Let U = e^4x du/dx = 4e^4x
    V = cot x dv/dx = -cose^2 x

    so dy/dx = cotx 4e^4x + e^4x (-cosec x)

    Now to simplifying;
    dy/dx = e^4x(4 cot x - cosec^2 x)


    Hmmm! I'm sure there's more to it. Can anyone help please.
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  2. #2
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    Re: Simplifying differential solutions - cotx e^4x

    Quote Originally Posted by froodles01 View Post
    Question is f(x) = e^4x cotx
    Fine, I'll use product rule;
    dy/dx = V du/dx * U dv/dx
    Let U = e^4x du/dx = 4e^4x
    V = cot x dv/dx = -cose^2 x
    You mean "-cosec^2 x" but that is obviously a typo.

    so dy/dx = cotx 4e^4x + e^4x (-cosec x)

    Now to simplifying;
    dy/dx = e^4x(4 cot x - cosec^2 x)


    Hmmm! I'm sure there's more to it. Can anyone help please.
    What you have is correct. Nothing more to it!
    Thanks from froodles01
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