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Find the derivative of sqrt(x)

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Answer
12x\boxed{\frac{1}{2\sqrt{x}}}

This matches the standard derivative formula for power functions when n=12n = \frac{1}{2}.

Problem: Find the derivative of f(x)=xf(x) = \sqrt{x}.

Steps

  1. Rewrite as a power
    f(x)=x12f(x) = x^{\frac{1}{2}}
  2. Apply the power rule
    f′(x)=12x12−1f'(x) = \frac{1}{2}x^{\frac{1}{2} - 1}
  3. Simplify the exponent
    f′(x)=12x−12f'(x) = \frac{1}{2}x^{-\frac{1}{2}}
  4. Rewrite with a positive radical
    f′(x)=12xf'(x) = \frac{1}{2\sqrt{x}}

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