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Math Help - Trig derivatives

  1. #1
    rmn
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    Trig derivatives

    ok so I think this is using chain rule again but i'm stuck at simplifying

    y= ((1+cosx)/(sinx))^(-1)

    i'm at

    -1 (1+cosx/sinx) ^(-2) times (-sinx^2 - cos x +cos x^2)/sinx^2

    and also

    y=sec^(2) pi x
    ok so there isn't any brackets around pix its just right beside sec^2 so i dont know how the chain rule would work?
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by rmn View Post
    ok so I think this is using chain rule again but i'm stuck at simplifying

    y= ((1+cosx)/(sinx))^(-1)

    i'm at

    -1 (1+cosx/sinx) ^(-2) times (-sinx^2 - cos x +cos x^2)/sinx^2

    and also

    y=sec^(2) pi x
    ok so there isn't any brackets around pix its just right beside sec^2 so i dont know how the chain rule would work?
    Ummm....
    y = \left ( \frac{1 + cos(x)}{sin(x)} \right ) ^{-1} = \frac{sin(x)}{1 + cos(x)}

    So
    \frac{dy}{dx} = \frac{cos(x) \cdot (1 + cos(x)) - sin(x) \cdot -sin(x)}{(1 + cos(x))^2}

    No need to do the chain rule, just use the quotient rule.

    -Dan
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  3. #3
    rmn
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    thanks
    for
    y=sec^(2) pi x
    do i just use the multiplication rule?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by rmn View Post
    thanks
    for
    y=sec^(2) pi x
    do i just use the multiplication rule?
    no, the chain rule (note, you would have to do it twice, once for sec^2 and one for pi x, post your solution so i can see if you get what i'm saying)
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  5. #5
    rmn
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    Quote Originally Posted by Jhevon View Post
    no, the chain rule (note, you would have to do it twice, once for sec^2 and one for pi x, post your solution so i can see if you get what i'm saying)
    theres no brackets around the pix though?

    well heres what i did

    sec^2 tan^2 (pi x) (pi)
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by rmn View Post
    theres no brackets around the pix though?
    what do you mean? (pi x) is what the secant is operating on, it is a linear function of x.

    sec^2 tan^2 (pi x) (pi)
    that is incorrect. recall the chain rule: \frac d{dx}f(g(x)) = f'(g(x))g'(x)
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  7. #7
    rmn
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    Quote Originally Posted by Jhevon View Post
    what do you mean? (pi x) is what the secant is operating on, it is a linear function of x.

    that is incorrect. recall the chain rule: \frac d{dx}f(g(x)) = f'(g(x))g'(x)

    is pi x g(x)?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by rmn View Post
    is pi x g(x)?
    no, \sec \left( \pi x \right) is g(x), the thing is, g(x) is itself a composite function, which is why you need the chain rule twice
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  9. #9
    rmn
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    Quote Originally Posted by Jhevon View Post
    no, \sec \left( \pi x \right) is g(x), the thing is, g(x) is itself a composite function, which is why you need the chain rule twice

    2 sec pi x sec ^2 tan^2 pi x ?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by rmn View Post
    2 sec pi x sec ^2 tan^2 pi x ?
    what is the derivative of sec(x)?
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  11. #11
    rmn
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    Quote Originally Posted by Jhevon View Post
    what is the derivative of sec(x)?
    secxtanx
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    Quote Originally Posted by rmn View Post
    secxtanx
    correct, so where did sec^2 tan^2 (pi x) come from?
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    is up to his old tricks again! Jhevon's Avatar
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    \frac d{dx} \sec^2 ( \pi x) = 2 \pi \sec (\pi x) \cdot \sec (\pi x) \tan (\pi x) = 2 \pi \sec^2 (\pi x) \tan (\pi x)


    now, can you tell me why?
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  14. #14
    rmn
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    Quote Originally Posted by Jhevon View Post
    \frac d{dx} \sec^2 ( \pi x) = 2 \pi \sec (\pi x) \cdot \sec (\pi x) \tan (\pi x) = 2 \pi \sec^2 (\pi x) \tan (\pi x)


    now, can you tell me why?

    in the question there is no brackets around pi x but u put brackets around it, or does it matter if there is
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by rmn View Post
    in the question there is no brackets around pi x but u put brackets around it, or does it matter if there is
    i put it for clarification, so you know what the secant is operating on
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