A student reasons that the functions f(x) = (x + 1)ln (x + 1) - x and g(x) = (x + 1)^1/3 must have the same derivative since she has entered f(x), g(x), f ′(x), and g′(x) into a graphing calculator, but only three graphs appear (see the figure). Is her reasoning correct? Are f ′(x) and g′(x) the same function? Explain.

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NORMAL FLOAT AUTO REAL DEGREE MP NORMAL FLOAT AUTO REAL DEGREE MP Ploti Plotz Plot3 NY1B(X+1)1n(X+1)-X INY28(X+1)/3 NY3B CY1)|x=x INY48CY2)|x=x INYS= NY6 = INY7= (A) (B)