calc

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how would i find the derivative of these?

f(x)=ln((√x)+1)

and

f(x)=ln(x+1/x-1)


thank u!!

  • calc -

    first one:
    remember that √x = x^(1/2)

    f ' (x) = 1/(√x + 1) ( (1/2)x^(-1/2)
    = 1/( 2x^(1/2) (√x)(√x + 1)
    = 1/( 2√x(√x + 1) or 1/(2(x+√x)

    2nd:

    not clear if you meant
    ln( x + 1/x - 1) --- the way you typed it , or
    ln( (x+1)/(x-1) ) --- I have a feeling that's the one, or
    ln( x + 1/(x-1) )

    I will read it as ln ((x+1)/(x-1))
    then this can be changed to
    ln(x+1) - ln(x-1)
    f ' (x) = 1/(x+1) - 1/(x-1)
    = (x-1 - (x+1))/((x+1)(x-1))
    = -2/((x+1)(x-1))

    notice how important brackets are ?

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