Let . Which of the following is…

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

Let f(x)=ln⁡(x21+ex)f(x)=\ln\left(\dfrac{x^2}{1+e^{x}}\right). Which of the following is f′(x)f'(x)? (a) 2x+ex1+ex\dfrac{2}{x}+\dfrac{e^{x}}{1+e^{x}} (b) 2x−ex1+ex\dfrac{2}{x}-\dfrac{e^{x}}{1+e^{x}} (c) (2x)(1+ex)−x2ex(1+ex)2\dfrac{(2x)(1+e^{x})-x^{2}e^{x}}{(1+e^{x})^{2}} (d) 1x−ex1+ex\dfrac{1}{x}-\dfrac{e^{x}}{1+e^{x}}

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