Special Derivatives. Derivatives of the remaining trig functions can be determined the same way. 

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Presentation transcript:

Special Derivatives

Derivatives of the remaining trig functions can be determined the same way. 

Find the derivative.

Basic Differentiation Rules 3 4 The Product Rule The Chain Rule 1 The derivative of the function f(x)=x is 1. These are the basic differentiation rules which imply all other differentiation rules for rational algebraic expressions. 2

Derived Differentiation Rules 6 5 The Quotient Rule. Follows from the Product Rule. Inverse Function Rule. Follows from the Chain Rule.

Special Function Rules

Proof of the Inverse Function Rule Inverse Function Rule Proof The Inverse Function Rule follows from this. Derivation differentiation rules for the inverse trigonometric functions are good examples of the usage of this formula. They will be presented later.

Inverse Trigonometric Functions Formula Proof

Inverse Trigonometric Functions Formula Proof

Differentiation of the Logarithm Formula Proof