The derivative of the function y = ln(1/x) can be calculated using the properties of logarithms and the rules of differentiation.
First, we can simplify the function using the logarithmic identity:
ln(1/x) = ln(1) – ln(x) = 0 – ln(x) = -ln(x).
So, we can rewrite our function as:
y = -ln(x)
Now, we need to differentiate this with respect to x. Using the derivative of the natural logarithm, we know:
dy/dx = -1/x.
Therefore, the derivative of y = ln(1/x) is:
dy/dx = -1/x
This means that for every unit increase in x, the value of y decreases by 1/x.