• as the slope of a curve
• as a rate of change or difference quotient
• as a function
• how to calculate from the difference quotient
• power rule of differentiation
• product and quotient rules
• chain rule
• implicit differentiation
• formal definitions and theorems

The Derivative: as a rate of change or difference quotient

	Best affine approximations, derivatives, and rates of change © Dan Sloughter 2000
	Define slope of tangent line as limit of slopes of secant lines © Dorothy Wallace etc.
	Differentiability © Daniel R. Cole
	Find slope of tangent line to y = x2 at (1,1) © Dorothy Wallace etc.
	Find slope of tangent line to y = √x at x = 4 © Dorothy Wallace etc.
	Find the equation for the tangent line of 4x2 + 10x + 5 at the point (2,1) using the limit definition of the derivative © Dorothy Wallace etc.
	Compute the derivative of f(x) = √(x + 2) using the limit definition of derivative © Dorothy Wallace