Using differentials find dy and delta y when y=7/x and dx=delta x =1

Answer 1

Perhaps you mean x = delta x = 1 ???

y = 7 x^-1
dy/dx = 7 (-1)x^-2 = -7 x^-2

if x = 1
y = 7/1 = 7
dy/dx = -7
delta y = -7 delta x
if delta x = 1
delta y = -7
Y + delta Y = 7-7 = 0

real answer
y (2) = 7/2 = 3.5