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    how is the differential of 1+tan2(4x)

    8*tan(4x)*sec2(4x)
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    Because the differential of Tan is Sec^2
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    (Original post by jsmith6131)
    how is the differential of 1+tan2(4x)

    8*tan(4x)*sec2(4x)
    Term-by-term differentiation with the chain rule on the second term twice. If it's not immediately clear, let y=1+\tan ^2(4x) and u=\tan 4x so y=1+u^2.

    Note that \dfrac{dy}{dx} = \dfrac{dy}{du} \times \dfrac{du}{dx}, the RHS of which should be more straightforward to evaluate.
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    Note that  1+tan^2(4x) \equiv sec^2(4x)

    Might be easier to differentiate that way, well it would be for me
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    so
    4*sec(4x)*sec(4x)*tan(x)
    where do I get
    8... from?
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    oh
    got it
    u2 goes to 2u
    sec4x goes to 4sec(4x)tan(4x)
    2*sec(4x)*sec(4x)*tan(4x)
 
 
 

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