Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §6.4 Logarithms, #70 · Calculus · Differentiation rules

The slope of … comes two ways from …: 1 Logarithmic differentiation…

The slope of $p = x^{x}$ comes two ways from $ln p = x ln x$ :
1 Logarithmic differentiation (LD): Compute $(ln p)^{'}$ and multiply by $p$ .
2 Exponential differentiation (ED): Write $x^{x}$ as $e^{x l n x}$ , take its derivative, and put back $x^{x}$ .

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §6.4 Logarithms, #70

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