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Algebra

Composite functions- Home
- UK Year 13 Maths
- Derivatives

Still Confused?

Try reviewing these fundamentals first.

Algebra

Composite functionsStill Confused?

Try reviewing these fundamentals first.

Algebra

Composite functionsNope, I 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?

24.

Derivatives

24.1

Definition of derivative

24.2

Power rule

24.3

Slope and equation of tangent line

24.4

Chain rule

24.5

Derivative of trigonometric functions

24.6

Derivative of exponential functions

24.7

Product rule

24.8

Quotient rule

24.9

Implicit differentiation

24.10

Derivative of inverse trigonometric functions

24.11

Derivative of logarithmic functions

24.12

Higher order derivatives

24.13

Tangent and concavity of parametric equations

We have over 760 practice questions in UK Year 13 Maths for you to master.

Get Started Now24.1

Definition of derivative

24.2

Power rule

24.3

Slope and equation of tangent line

24.4

Chain rule

24.5

Derivative of trigonometric functions

24.6

Derivative of exponential functions

24.7

Product rule

24.8

Quotient rule

24.9

Implicit differentiation

24.10

Derivative of inverse trigonometric functions

24.11

Derivative of logarithmic functions

24.12

Higher order derivatives