Exponential and logarithmic functions
Growth, decay and the natural log, the functions behind e.
Natural exponential function
f(x) = e^x
The natural exponential function e^x: what e is, its graph, why it is its own derivative and integral, key limits, series and worked examples.
Exponential functions
f(x) = b^x, \quad b > 0,\ b \ne 1
Exponential functions f(x) = b^x: growth and decay graphs, properties, the derivative b^x ln b, the integral b^x / ln b + C and worked examples.
Natural logarithm
f(x) = \ln x
The natural logarithm ln x: its graph, log rules, why its derivative is 1/x, the integral x ln x - x + C, and worked calculus examples.
Logarithmic functions
f(x) = \log_b x, \quad b > 0,\ b \ne 1
Logarithmic functions log_b x: definition, graphs, log rules, change of base, the derivative 1/(x ln b), the integral and worked examples.
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