Special derivatives
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Special Derivatives PowerPoint PPT Presentation


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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.

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Special Derivatives

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Special derivatives

Special Derivatives


Special derivatives

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

p


Special derivatives

Find the derivative.


Basic differentiation rules

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

Derived Differentiation Rules

The Quotient Rule. Follows from the Product Rule.

5

6

Inverse Function Rule. Follows from the Chain Rule.


Special function rules

Special Function Rules

7

12

8

13

9

14

10

11


Proof of the inverse function rule

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

Inverse Trigonometric Functions

Formula

Proof


Inverse trigonometric functions1

Inverse Trigonometric Functions

Formula

Proof


Differentiation of the logarithm

Differentiation of the Logarithm

Formula

Proof


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