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.

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Find the derivative. determined the same way.


Basic differentiation rules
Basic Differentiation Rules determined the same way.

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 determined the same way.

The Quotient Rule. Follows from the Product Rule.

5

6

Inverse Function Rule. Follows from the Chain Rule.


Special function rules
Special Function Rules determined the same way.

7

12

8

13

9

14

10

11


Proof of the inverse function rule
Proof of the Inverse Function Rule determined the same way.

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 determined the same way.

Formula

Proof


Inverse trigonometric functions1
Inverse Trigonometric Functions determined the same way.

Formula

Proof


Differentiation of the logarithm
Differentiation of the Logarithm determined the same way.

Formula

Proof


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