To find the differential dy, we start with the function:
y = 1/x
The differential dy can be found using the formula:
dy = y’ * dx
First, we need to calculate the derivative y’:
y’ = -1/x^2
Now, we plug in the given value of x which is 0. Unfortunately, calculating the derivative at x=0 leads to an undefined situation since you cannot divide by zero.
However, if we evaluate the differential for a nearby value, let’s say x approaches 0, but we’ll use x=0.01 for our calculation. Then:
y’ = -1/(0.01)^2 = -100
Next, we substitute y’ and dx = 0.02 into the differential formula:
dy = (-100) * 0.02 = -2
So, considering a value close to zero, the differential dy is approximately -2.