Standard Space: y(x)
Slope y'(2) = 6.77
Logarithmic Space: ln(y)
Slope d/dx[ln y] = 1.69
Evaluation Point (x)
2.0000
Log Space Side d/dx[ln y]
1.6931
Exact Tangent Slope y'(x)
6.7726
David Jerison Method Intuition
Directly differentiating power towers like x^x is impossible with standard power or exponential rules alone because both base and exponent vary. By applying ln(y), power relationships turn into products, and rational quotients turn into subtractions. The derivative in logarithmic space is simply y'/y, meaning the true slope is obtained by scaling the log-space slope back up by y.