Let f(x)=sqrtx. f^(')(x)=

Recall Power Rule: Recall the power rule for differentiation, which states that if f(x) = x^n, then f'(x) = n*x^(n-1).Rewrite in Exponent Form: Rewrite the square root function in exponent form: f(x) = x^(1/2).Apply Power Rule: Apply the power rule to differentiate f(x) = x^(1/2). This gives us f'(x) = (1/2)*x^((1/2)-1).Simplify Exponent: Simplify the exponent in the derivative: f'(x) = (1/2)*x^(-1/2).Rewrite in Radical Form: Rewrite the derivative in radical form to avoid negative exponents: f'(x) = (1/2)*(1/sqrt(x)).Combine Constants: Combine the constants and the radical to get the final simplified form of the derivative: f'(x) = 1/(2*sqrt(x)).

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Let $f(x)=\sqrt{x}$ . $\newline$ $f^{\prime}(x)=$

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Q. Let

f(x)=\sqrt{x}

\newline

f^{\prime}(x)=

Recall Power Rule: Recall the power rule for differentiation, which states that if $f(x) = x^n$ , then $f'(x) = n \cdot x^{(n-1)}$ .
Rewrite in Exponent Form: Rewrite the square root function in exponent form: $f(x) = x^{\frac{1}{2}}$ .
Apply Power Rule: Apply the power rule to differentiate $f(x) = x^{\frac{1}{2}}$ . This gives us $f'(x) = \left(\frac{1}{2}\right)\cdot x^{\left(\frac{1}{2}-1\right)}$ .
Simplify Exponent: Simplify the exponent in the derivative: $f'(x) = (\frac{1}{2})\cdot x^{(-\frac{1}{2})}$ .
Rewrite in Radical Form: Rewrite the derivative in radical form to avoid negative exponents: $f'(x) = \frac{1}{2}\cdot\frac{1}{\sqrt{x}}$ .
Combine Constants: Combine the constants and the radical to get the final simplified form of the derivative: $f'(x) = \frac{1}{2\sqrt{x}}$ .