Exponential and Logarithmic Derivatives: Four Rules and x^x

This lesson builds the four standard derivative rules for exponential and logarithmic functions, with the base and domain conditions that earn exam credit. For differentiable $g$, it covers , $\ln (g(x))$, , and , where , , and logarithm inputs are positive. 1

Three complete examples show the exponential Chain Rule, a tangent slope for , and logarithmic differentiation for . The final checklist targets the most common lost factors: the inner derivative, $\ln b$, and the positive-input condition for logarithms. 2