Let y=e^ (x/5).

Find the differential dy when x=3 and dx=0.3

Find the differential dy when x=3 and dx=0.01

Y = e^ (x/5)

d y / d x = 1/5 * e^ (x/5)

d y = 1/5 * e^ (x/5) d x

A) x = 3, d x = 0.3

d y = 1/5 * e^ (0.6) * 0.3 = 0.06 * e^ (0.6)

B) x = 3, d x = 0.01

d y = 1/5 * e^ (0.6) * 0.01 = 0.002 * e^ (0.6)