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Differentiation of Logarithmic Expressions

The following table contains working examples of the differentiation of some basic logarithmic formulas.

y = ax

dy/dx = ax . Ln(a)

y = Ln(x)
y = Ln(a.x)
y = Ln(x/a)

dy/dx = 1/x

y = Ln(a/x)

dy/dx = x

y = Ln(xa)

dy/dx = a/x

y = ex

dy/dx = ex, d²y/dx² = ex, etc.

y = e-x

dy/dx = -e-x, d²y/dx² = e-x, etc.

y = eax

dy/dx = aeax, d²y/dx² = a²eax, etc.

y = e-ax

dy/dx = -ae-ax, d²y/dx² = a²e-x, etc

Further Reading

You will find further reading on this subject in reference publications(19)

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