AP Calculus ABeasymcq1 pt

If f(x)=arctan(2x)f(x)=\arctan(2x), then f(x)=f'(x)=

A.21+4x2\dfrac{2}{1+4x^2}
B.11+4x2\dfrac{1}{1+4x^2}
C.21+2x2\dfrac{2}{1+2x^2}
D.21+x2\dfrac{2}{1+x^2}

Explanation

Core Concept

Start with 11+(2x)2\frac{1}{1+(2x)^2}, then multiply by the inner derivative 2. The result is 21+4x2\frac{2}{1+4x^2}.

Correct Answer

A21+4x2\dfrac{2}{1+4x^2}

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