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Math Help - Trig/Chain Rule Derivatives

  1. #1
    Member VitaX's Avatar
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    Trig/Chain Rule Derivatives

    I'm just wondering if theres a difference between finding the derivative of Sin^3(2x+1) and Sin(2x+1)^3 and if so whats the main difference?
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  2. #2
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    Quote Originally Posted by VitaX View Post
    I'm just wondering if theres a difference between finding the derivative of Sin^3(2x+1) and Sin(2x+1)^3 and if so whats the main difference?
    No because they are one and the same.

    sin^n \theta = (sin \theta)^n \: \: \: \: , \: \: \: n \in \mathbb{Z^+}
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    Quote Originally Posted by VitaX View Post
    I'm just wondering if theres a difference between finding the derivative of Sin^3(2x+1) and Sin(2x+1)^3 and if so whats the main difference?
    None. They are the same thing just different notation. Writing \sin^n(x) seems to cause less confusion from my experience.
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  4. #4
    Member VitaX's Avatar
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    When I input them both on this wolfram site I get different answers

    http://www.wolframalpha.com/input/?i=d/dx+%28sin%282x%2B1%29%29^3
    http://www.wolframalpha.com/input/?i=d/dx+sin%28%282x%2B1%29^3
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  5. #5
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    e^(i*pi)'s Avatar
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    It could be seeing the second one as sin[(2x+1)^3]
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  6. #6
    Member VitaX's Avatar
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    Well say you have Sin^2(2x+2) and sin(2x+2)^2 I thought the difference was the first equation the entire thing is squared but the second equation only (2x+2) is squared. That wrong?
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