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Algebra

Composite functions- Home
- AU Maths Extension 1
- Derivatives

Still Confused?

Try reviewing these fundamentals first

Algebra

Composite functionsStill Confused?

Try reviewing these fundamentals first

Algebra

Composite functionsNope, got it.

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Get Started Now- Lesson: 131:49
- Lesson: 2a9:40
- Lesson: 2b10:21
- Lesson: 3a11:16
- Lesson: 3b1:10
- Lesson: 3c2:19

We have studied the notion of average rate of change thus far, for example, change in position over time (velocity), average change in velocity over time (acceleration) etc. However, what if we are interested in finding the instantaneous rate of change of something? To answer this, we will first learn about the concept of the definition of derivative in this section, as well as how to apply it.

Basic Concepts: Composite functions

Definition of Derivative

$f'\left( x \right) = \;_{h \to 0}^{\;lim}\frac{{f\left( {x + h} \right) - f\left( x \right)}}{h}$

$f'\left( x \right) = \;_{h \to 0}^{\;lim}\frac{{f\left( {x + h} \right) - f\left( x \right)}}{h}$

- 1.Find the derivative of the given function using the definition of derivative.

$f\left( x \right) = {x^3} - 5x + 6$ - 2.
**Definition of derivative with irregular functions**

Find the derivative of the following functions using the definition of derivative.

a)$f(x)=\sqrt{x-2}$b)$f(x)=\frac{3-x}{2+x}$ - 3.
**Applications to definition of derivative**

Let $f(x)=4x^{\frac{1}{3}}$a)For when $x \neq 0$, find the derivative of $f(x)$.b)Show that $f'(0)$ does not exist.c)For what value(s) of $x$ does the vertical tangent line occur?

41.

Derivatives

41.1

Definition of derivative

41.2

Power rule

41.3

Slope and equation of tangent line

41.4

Chain rule

41.5

Derivative of trigonometric functions

41.6

Derivative of exponential functions

41.7

Product rule

41.8

Quotient rule

41.9

Derivative of inverse trigonometric functions

41.10

Derivative of logarithmic functions

41.11

Higher order derivatives

We have over 1640 practice questions in AU Maths Extension 1 for you to master.

Get Started Now41.1

Definition of derivative

41.2

Power rule

41.3

Slope and equation of tangent line

41.4

Chain rule

41.5

Derivative of trigonometric functions

41.6

Derivative of exponential functions

41.7

Product rule

41.8

Quotient rule

41.9

Derivative of inverse trigonometric functions

41.10

Derivative of logarithmic functions

41.11

Higher order derivatives