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How does one find the derivative of ln(x)?

Let

         y = ln(x)

Then

         x = e^y

[ ln(x) = ln(e^y) = y ln(e) = y*1 = y ]

Taking the derivative of this we get

         dx/dy = e^y

Taking the reciprocal we get

         dy/dx = 1/e^y = 1/x

So the derivative of ln(x) is

         d(ln(x))/dx = 1/x

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Degree: Mathematics (Masters) - Bristol University

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