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Methods of Differentiation — Part 2: Logarithmic and second-order derivatives

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Lesson

Methods of Differentiation, Part 2

How do we differentiate xxx^{x}?

In this lesson you will

  • Differentiate variable powers such as x to the power x by taking logarithms
  • Differentiate sums of variable powers and long products or quotients
  • Differentiate towers of powers
  • Find second-order derivatives of explicit, implicit and parametric functions
  • Prove a relation between y and its first two derivatives
  • y=xxy = x^{x}
Neither the power rule nor the exponential rule fits $x^{x}$.