Show that the derivative of ln(x) = 1/x
We can start by letting y = ln(x)
What we are trying to show is that dy/dx = 1/x
Since y = ln(x), then ey = eln(x) = x
Taking the derivative of each side of this equation will give us ey.dy/dx = 1
If we divide each side of this new equation by ey then we have that dy/dx = 1/ey = 1/x as required.
JC
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