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The Derivative of a Complex Fraction

SVCALC-C$BEBV

Consider the function:

$$f(x) = \dfrac{x }{ 1+ \dfrac{x}{1 + \dfrac{x}{ 1+\dfrac1x }}}$$

Find $f'(2)$.

A

$\dfrac{9}{13}$

B

$\dfrac{81 }{169}$

C

$\dfrac{14}{13}$

D

$\dfrac{12}{25}$