AP Calculus ABmediummcq1 pt

If f(x)=x2+1f(x)=\sqrt{x^2+1}, then f(x)=f'(x)=

A.xx2+1\dfrac{x}{\sqrt{x^2+1}}
B.12x2+1\dfrac{1}{2\sqrt{x^2+1}}
C.2xx2+1\dfrac{2x}{\sqrt{x^2+1}}
D.1x2+1\dfrac{1}{\sqrt{x^2+1}}

Explanation

Core Concept

The power rule gives 12(x2+1)1/2\frac{1}{2}(x^2+1)^{-1/2}, and the inner derivative is 2x2x. Multiplying gives x(x2+1)1/2=xx2+1x(x^2+1)^{-1/2}=\frac{x}{\sqrt{x^2+1}}.

Correct Answer

Axx2+1\dfrac{x}{\sqrt{x^2+1}}

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