Page 1: Advanced Differentiation Techniques

This page presents a detailed overview of various differentiation techniques and their applications in calculus. The content covers fundamental rules and their practical implementations through worked examples.

Definition: The product rule states that if y = uv, then the derivative is found by multiplying each function by the derivative of the other and adding the results.

Example: When differentiating x²cosx, using the product rule: Let u = x² and v = cosx, then dy/dx = 2xcosx - x²sinx

Highlight: Chain rule applications are particularly important when dealing with composite functions, especially with logarithmic and trigonometric expressions.

Vocabulary: Implicit differentiation refers to the technique of differentiating equations where y is not explicitly solved for in terms of x.

Quote: "Product rule is when you have a product of functions and not one type of function."

The page elaborates on various differentiation techniques including:

• Basic differentiation formulas for trigonometric functions
• Chain rule applications with detailed examples
• Product rule implementation with step-by-step solutions
• Implicit differentiation methods
• Inverse function differentiation
• Quotient rule applications for fractional expressions