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A particle moves along the curve so that its -coordinate increases at the constant rate of units per second. How fast is its angle of inclination changing when ?

(As shown in the diagram at right, is the angle between the segment joining the point to the origin and the -axis.)

What are the opposite and adjacent sides here?

To obtain , use implicit differentiation in terms of , since the -coordinate and are changing over time.

Increasing exponential curve, with point on the curve in first quadrant, segment connects the point to the origin, angle between segment and positive x axis, labeled theta.