3.2 Differentiation Chapter Contents

By the end of this chapter you will have:

$\diamond$ learned the notion of tangent to a graph;

$\diamond$ learned how to define the derivative as a limit of difference quotients;

$\diamond$ seen examples of functions with and without derivatives;

$\diamond$ revised Leibniz’s rules for calculating derivatives;

$\diamond$ found the derivative of the exponential equation and used it to solve the growth and decay differential equation;

$\diamond$ found derivatives of inverse functions by the inverse function rule;

$\diamond$ computed related rates of change by the chain rule;

$\diamond$ used logarithmic differentiation;

$\diamond$ learned the dynamical interpretation of first and second derivative as velocity and acceleration;

$\diamond$ computed higher order derivatives;

$\diamond$ solved the differential equation for simple harmonic motion.