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Algebra

Composite functions- Home
- Differential Calculus
- Differentiation

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?

2.

Differentiation

2.1

Definition of derivative

2.2

Estimating derivatives from a table

2.3

Power rule

2.4

Slope and equation of tangent line

2.5

Chain rule

2.6

Derivative of trigonometric functions

2.7

Derivative of exponential functions

2.8

Product rule

2.9

Quotient rule

2.10

Implicit differentiation

2.11

Derivative of inverse trigonometric functions

2.12

Derivative of logarithmic functions

2.13

Higher order derivatives

We have over 170 practice questions in Differential Calculus for you to master.

Get Started Now2.1

Definition of derivative

2.3

Power rule

2.4

Slope and equation of tangent line

2.5

Chain rule

2.6

Derivative of trigonometric functions

2.7

Derivative of exponential functions

2.8

Product rule

2.9

Quotient rule

2.10

Implicit differentiation

2.11

Derivative of inverse trigonometric functions

2.12

Derivative of logarithmic functions

2.13

Higher order derivatives