Check out this topic in the following free, online textbooks:
The Limit Definition of the Derivative
Short explanations:
Difference Quotient and Average Rate of Change:
Limit Definition of Derivative: BrightStorm
Finding the Equation of the Tangent Line: Math BFF
Longer, lecture style: Prof. RobBob Prof. Leonard
Basic Derivative Rules (Power, Product, Quotient)
Short explanations: MySecretMathTutor
Longer, lecture style:
Crystal Clear Maths Prof. RobBob Prof. Leonard
The Chain Rule
Short explanations: IntegralCALC
Longer, lecture style:
Crystal Clear Maths Prof. RobBob Prof. Leonard
Advanced topics:
Functions Inside the Exponent Crystal Clear Maths
Logarithmic Differentiation
Videos for Specific probelms: MathisPower4U's Calculus I Video Library (middle column)
Online Tutorials (including exercises with solutions)
Problem Sets with solutions
Drill problems for finding the derivative of a function using the definition of a derivative.
Drill problems for differentiation using the product rule. (Algebraic and exponential functions).
Drill problems for differentiation using the quotient rule.
Drill problems for differentiation using the product rule. (Emphasis on trigonometric functions).
Drill problems for differentiation using the quotient rule. (Emphasis on trigonometric functions).
Extra Drill problems for differentiation using the product rule.
Drill problems for differentiation using the chain rule.
Drill on applying logarithmic differentiation.
eCalculus.org and UC Davis Math
Problems on the limit definition of the derivative
Problems on the chain rule
Problems on the product rule
Problems on the quotient rule
Problems on differentiation of trigonometric functions
Problems on differentiation of inverse trigonometric functions
Problems on logarithmic differentiation
Free Worksheets (with solutions)
Free Quizzes (with solutions)
Quiz on finding the derivative of functions overall.