Question

Let y=e^(x/9).

a) Find the differential dy.
dy =

b) Evaluate dy if x=0 and dx=−0.03.
dy =

Answer 1

dy = (1/9) e^(x/9) dx

at x=0, dx=-.03, we have

dy = (1/9)(1)(-.03) = -1/300

What his means is that if you draw the graph of y=e^(x/9) and then draw the tangent line at x=0, if you move along that line horizontally to the left by .03 (dx), you will move vertically down by 1/300 (dy).