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Algebra

Composite functions- Home
- Higher 2 Maths
- Derivatives

Still Confused?

Try reviewing these fundamentals first.

Algebra

Composite functionsStill Confused?

Try reviewing these fundamentals first.

Algebra

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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?

17.

Derivatives

17.1

Definition of derivative

17.2

Power rule

17.3

Gradient and equation of tangent line

17.4

Chain rule

17.5

Derivative of trigonometric functions

17.6

Derivative of exponential functions

17.7

Product rule

17.8

Quotient rule

17.9

Implicit differentiation

17.10

Derivative of inverse trigonometric functions

17.11

Derivative of logarithmic functions

17.12

Higher order derivatives

We have over 700 practice questions in Higher 2 Maths for you to master.

Get Started Now17.1

Definition of derivative

17.2

Power rule

17.3

Gradient and equation of tangent line

17.4

Chain rule

17.5

Derivative of trigonometric functions

17.6

Derivative of exponential functions

17.7

Product rule

17.8

Quotient rule

17.9

Implicit differentiation

17.10

Derivative of inverse trigonometric functions

17.11

Derivative of logarithmic functions

17.12

Higher order derivatives