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# Special Derivatives PowerPoint PPT Presentation

Special Derivatives. Derivatives of the remaining trig functions can be determined the same way. p. Find the derivative. Basic Differentiation Rules . The derivative of the function f( x )= x is 1. 1. 2. 3. The Product Rule. The Chain Rule. 4.

Special Derivatives

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## Special Derivatives

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

p

Find the derivative.

### Basic Differentiation Rules

The derivative of the function f(x)=x is 1.

1

2

3

The Product Rule

The Chain Rule

4

These are the basic differentiation rules which imply all other differentiation rules for rational algebraic expressions.

### Derived Differentiation Rules

The Quotient Rule. Follows from the Product Rule.

5

6

Inverse Function Rule. Follows from the Chain Rule.

7

12

8

13

9

14

10

11

### 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.

Formula

Proof

Formula

Proof

Formula

Proof