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    use two substitutions to find

    d/dx (e^rt(1-x^2))

    thanks!
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    u = 1-(x^2)
    v = u^(1/2)
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    chain rule...

    dy/dx = (dy/du)(du/dx)

    however, as we are doing two substitutions, we'll need....

    dy/dx = (dy/du)(du/dx)
    dy/du = (dy/dv)(dv/du)

    dy/dx = (dy/dv)(dv/du)(du/dx)

    y = (e^rt(1-x^2))
    u = 1-(x^2)
    v = u^(0.5)

    what we need to differentiate...

    y = e^v
    v = u^(0.5)
    u = 1-(x^2)

    dy/dv = (e^v)
    dv/du = (0.5)u^-0.5
    du/dx = -2x

    dy/dx = (dy/dv)(dv/du)(du/dx)
    dy/dx = [e^{(1-x^2)^0.5)}][0.5{(1-x^2)^-0.5}][-2x]

    be as well getting someone else to check...
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    (Original post by sarah12345)
    use two substitutions to find

    d/dx (e^rt(1-x^2))

    thanks!
    Q.) Find d/dx [e^rt(1 - x^2)]
    Let the function we want to differentiate be y = [e^Sqrt(1 - x^2)]

    Sub 1.) Let u = (1 - x^2) ---> du/dx = -2x
    Sub 2.) Let v = Sqrt(u) = u^1/2 ---> dv/du = 1/2.u^(-1/2) = 1/[2Sqrt(u)]
    Hence: y = e^v ---> dy/dv = e^v

    Hence: d/dx [e^Sqrt(1 - x^2)] = dy/dx = dy/dv * dv/du * du/dx = e^v * 1/[2Sqrt(u)] * (-2x) = -{2xe^[Sqrt(1 - x^2)]}/[2Sqrt(1 - x^2)]

    ---> d/dx [e^rt(1 - x^2)] = -{xe^[Sqrt(1 - x^2)]}/[Sqrt(1 - x^2)]
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    (Original post by Nima)
    Q.) Find d/dx [e^rt(1 - x^2)]
    Let the function we want to differentiate be y = [e^Sqrt(1 - x^2)]

    Sub 1.) Let u = (1 - x^2) ---> du/dx = -2x
    Sub 2.) Let v = Sqrt(u) = u^1/2 ---> dv/du = 1/2.u^(-1/2) = 1/[2Sqrt(u)]
    Hence: y = e^v ---> dy/dv = e^v

    Hence: d/dx [e^Sqrt(1 - x^2)] = dy/dx = dy/dv * dv/du * du/dx = e^v * 1/[2Sqrt(u)] * (-2x) = -{2xe^[Sqrt(1 - x^2)]}/[2Sqrt(1 - x^2)]

    ---> d/dx [e^rt(1 - x^2)] = -{xe^[Sqrt(1 - x^2)]}/[Sqrt(1 - x^2)]
    thanks alot!!
    one thing i dont understand is why do you have to mave 2 substitutions why not just say that u=srt(1-x^2)??????
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    (Original post by sarah12345)
    thanks alot!!
    one thing i dont understand is why do you have to mave 2 substitutions why not just say that u=srt(1-x^2)??????
    anyone?
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    (Original post by sarah12345)
    thanks alot!!
    one thing i dont understand is why do you have to mave 2 substitutions why not just say that u=srt(1-x^2)??????
    That works if you can differentiate sqrt(1 - x^2) in your head - a useful skill!
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    (Original post by Nima)
    Because the question asked me to use 2 substitutions, so I did.
    ok thanks its just i was wonderin if there were certain times when u had to do two substiituitions for it to work.

    thanks alot for all the help
 
 
 
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