textbook-theory · English
The Natural Logarithm Function (Section 6.2)
Section 6.2 of Dan Sloughter's open calculus textbook 'Difference Equations to Differential Equations,' covering the natural logarithm function as the inverse of the exponential function. The section derives properties of log(x) including algebraic identities, the derivative (d/dx log(x) = 1/x), integral formulas, the Taylor series expansion about x=1, and the power rule extended to irrational exponents. Worked examples include differentiation via the chain rule, integration by substitution (tan(x), sec(x)), integration by parts for log(x)dx, and graphical analysis of y = log(x).
natural logarithmcalculusdifferentiationintegration