Question

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

Answer 1

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)