Using chain and power rules, dy/dx = 1/x; while dy/du = 1/u. When graphed as y=ln(x), the graph is indicated as per the attached.
It is right to state that the inclusion of the variable 'u' alters the function in that log(x) is a natural logarithm
What is a natural logarithm?
The natural logarithm of an integer is its logarithm to the root of the irrational and transcendental variable e, which is roughly equal to 2.718281828459.
First there is the input of y = log(ux)
Then, y = log(u) + log (x) - These are al alternate forms deduced based on the assumption that u, x, and y are all positive.
u!=0, x = 1/u
Therefore, the root for the variable u = 1/x
Learn more about natural logarithms at:
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