APFIVE Quotient Rule for Differentiation
Consider the function $$u(t)=\frac{t}{t+1}$$. Using the quotient rule, which of the following equations correctly represents its derivative $$u'(t)$$? (Do not use a calculator.)
A
$$u'(t)=\frac{1}{t+1}$$
B
$$u'(t)=\frac{t}{(t+1)^2}$$
C
$$u'(t)=\frac{1}{(t+1)^2}$$
D
$$u'(t)=\frac{-1}{(t+1)^2}$$
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