If f(x) = sqrt(x), what is f'(x)?
Model Answer & Options
Source: Extra Practice1 / (2 * sqrt(x))
2 * sqrt(x)
1 / sqrt(x)
-1 / (2 * sqrt(x))
Explanation
f(x) can be written as x^(1/2). Applying the power rule: d/dx(x^n) = n*x^(n-1), we get (1/2)*x^(1/2 - 1) = (1/2)x^(-1/2) = 1 / (2sqrt(x)). Option B is the reciprocal. Option C is missing the factor of 1/2. Option D incorrectly includes a negative sign.
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