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p5 differentiation watch

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    how do i differentiate arsechx, arcothx and arcosechx

    cheers.
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    y = arsechx
    sechy = x

    Now implicit differentiation and see how you get on from there...

    (same for the others)
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    yeah ive done that much but I get 1/-tanhxssechx for the first one, what do I do with that?
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    i mean 1/-tanhysechy
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    (Original post by Bebop)
    i mean 1/-tanhysechy
    Use the identity (tanhy)^2+1=(sechy)^2 to rewrite it in terms of sechy and hence x.
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    And at the same time your learning which substitution to use to integrate the ugly looking result!
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    ah right so for the first one its 1/x(x^2 - 1)^1/2 yah?
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    (Original post by Bebop)
    how do i differentiate arsechx, arcothx and arcosechx

    cheers.
    y=sech^-1 x
    sechy =x
    -sechytanhydy/dx=1

    dy/dx=-1/sechytanhy...............(1)
    cosh^2 y -sinh^2 y=1
    => 1-sech^2y=tanh^2y
    (1) becomes
    dy/dx=-1/x(1-x^2)^1/2
    ii)
    y=cosech^-1 x
    cosechy =x
    -cosechycothydy/dx=1

    dy/dx=-1/cosechycothy...............(2)
    cosh^2 y -sinh^2 y=1
    => 1+cosech^2y=coth^2y
    (2) becomes
    dy/dx=-1/x(1+x^2)^1/2

    iii)
    y=coth^-1 x
    cothy =x
    -cosech^2ydy/dx=1

    dy/dx=-1/cosech^2y...............(2)
    cosh^2 y -sinh^2 y=1
    => coth^2y-1=cosech^2y
    (2) becomes
    dy/dx=-1/(x^2-1)=1/(1-x^2)
 
 
 
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