Ira S. answered • 09/22/14

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Finding rates is taking the derivative with respect to time....dy/dt and dx/dt.

y=ln(2+e^-2x)

dy/dt = 1/( 2 + e^(-x) ) *(-e ^ (-x) ) dx/dt

you know dx/dt = 3 and you're looking for when x =1, so,

dy/dt = 1/ ( 2 + e^-1) * (-e^-1) * 3

dy/dt = 1/ (2+e^-1) * -1/e^1 * 3

dy/dt = -3/( 2e^1 +1)

This is the same as your answer.