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    Can someone help me with the following questions please?

    1) Given that y = ln (x + √(x² +1)),
    show that: dy/dx = 1/ √(x²+1)

    2 Find
    a) d/dx (ln(lnx)
    b) d/dx (sin(sinx))

    3) show from first principle that if y = cosx then the diferrential is -sinx

    Thanks to anyone that can help me!!
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    For (3) I have a good resource: http://mathscentre.ac.uk/resources/w...principles.pdf
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    1) Given that y = ln (x + √(x² +1)),,show that: dy/dx = 1/ √(x²+1)
    Use the chain rule with u = x + √(x² +1), then y = lnu
    a) d/dx (ln(lnx)
    Use the chain rule with u = lnx, then y = lnu
    b) d/dx (sin(sinx))
    Use the chain rule with u = sinx, then y = sinu
    3) show from first principle that if y = cosx then the diferrential is -sinx
    Check page 4
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    (Original post by latin.snake)
    Can someone help me with the following questions please?

    1) Given that y = ln (x + √(x² +1)),
    show that: dy/dx = 1/ √(x²+1)
    That looks like a hyperbolic function...

    sinh-1 x = ln (x +√(x² +1))

    so y = sinh-1 x
    x = sinh y
    dx/dy = cosh y
    dy/dx = 1/cosh y

    cosh y = √(1+sinh² x)

    so dy/dx = 1/√(1+sinh² x)

    x = sinh y

    dy/dx = 1/√(1+x²)


    I hope thats right, otherwise I'm failing FP2 tomorrow! It might not be the easiest way to do it but I think its pretty nifty.
 
 
 
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