AP Calculus ABmediummcq1 pt

If f(x)=xf(x)=\sqrt{x}, then f(x)=f'(x)=

A.1x\dfrac{1}{\sqrt{x}}
B.x2\dfrac{\sqrt{x}}{2}
C.12x\dfrac{1}{2\sqrt{x}}
D.2x\dfrac{2}{\sqrt{x}}

Explanation

Core Concept

Rewrite x=x1/2\sqrt{x}=x^{1/2}, so f(x)=12x1/2=12xf'(x)=\dfrac{1}{2}x^{-1/2}=\dfrac{1}{2\sqrt{x}}. The power rule works with fractional exponents.

Correct Answer

C12x\dfrac{1}{2\sqrt{x}}

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