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 e= 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 ethen we have that dy/dx = 1/ey = 1/x as required.

JC
Answered by James C. Maths tutor

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