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Derivative of a fraction inside a radical

  1. Jul 7, 2014 #1


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    f(z) = sq. rt of z-1 / z+1 --- both numerator and denominator are inside the radical.

    I can write it as (z-1)^1/2 over (z+1)^1/2, right? If I simplify it using derivative of a quotient. Should I simplify (z-1)^1/2 and (z+1)^1/2 as whole numbers and multiply them to other terms, including adding the exponents? The teach said I couldn't because the one-halves are actually square roots so I cant count them as exponents. Help?
  2. jcsd
  3. Jul 7, 2014 #2


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    √x = x^1/2; when taking derivatives of radicals you should always convert them to exponents.
  4. Jul 7, 2014 #3


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    You can differentiate [tex]\sqrt[2]{\frac{z- 1}{z+ 1}[/tex] by treating it as [tex]\frac{(z- 1)^{1/2}}{(z+ 1)^{1/2}}[/tex] using the quotient theorem, the chain rule, and the power rule, in that order. Or think of it as [tex]\left(\frac{z-1}{z+1}\right)^{1/2}[/tex] using the same rule in a different order. Or think of it as [tex](z- 1)^{1/2}(z+ 1)^{1/2}[/tex] and use the product rule rather than the quotient rule.
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