Differentiation of Logarithmic Expressions

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

The Formulas

y = ax	dy/dx = a^x . 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(x^a)	dy/dx = a/x
y = e^x	dy/dx = e^x, d²y/dx² = e^x, etc.
y = e^-x	dy/dx = -e^-x, d²y/dx² = e^-x, etc.
y = e^ax	dy/dx = ae^ax, d²y/dx² = a²e^ax, 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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