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Study note

Islombek

United States of America

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Algebra 2

Arithmetic

Understanding Differentiation 

Polynomial graphs

Putting it all together

Study Note: Understanding Differentiation
INTRODUCTION:
• Differentiation is a mathematical concept that
deals with calculating the rate at which a quantity
changes.
It is a fundamental concept in calculus and has
various real-life applications.
• In this study note, we will discuss the visual
representation of differentiation and strategies
for understanding it.
Visual Representation of Differentiation:
• To understand differentiation, one must first
understand the concept of the slope of a curve.
• The slope of a curve at a point is the rate at which
the curve is changing at that point.
• Differentiation is simply finding the slope of a
curve at any given point.
Strategies for Understanding Differentiation
1. Understand basic differentiation rules:
Differentiation rules are basic formulas used to find
the derivative of a function. Some of the basic rules
include the power rule, product rule, quotient rule,
and chain rule. 2. Practice with examples:
• To gain a better understanding of differentiation,
practice solving problems using different methods
and rules.
• Work through different examples with varying
levels of difficulty to build your confidence and
competence.
3. Understand the relationship between
differentiation and graphs:
• Graphs can be used to visually represent the
differentiation of a function.
• By understanding how differentiation affects the
graph of a function, you can gain a deeper
understanding of the concept.
Example of Differentiation
Let's take a simple function:
• f(x) = x², and find its derivative using the power
rule. According to the power rule, if f(x) = x¹,
then f'(x) = nxn-1.
• Therefore, the derivative of f(x) = x² is f'(x) = 2x.
Exercises: 1. Find the derivative of f(x) = 3x^4 + 2x^3 - 5x^2
using the sum and power rules.
2. Find the derivative of f(x) = sin(x) using the
chain rule.
3. Find the slope of the curve y = x^3 at the point
(2,8).
LIST OF FORMULAS:
Constant Rule
Power Rule
Product Rule
Quotient Rule
Chain Rule
d
dx
d
dx
d
dx
[C] = 0
dx
xn = nxn-1
[f(x)g(x)] = f'(x)g(x) + f(x)g'(x)
d f(x) g(x)f'(x) - f(x)g'(x)
dx g(x)
[g(x)]²
[f(g(x))] = f'(g(x)) g'(x)
=

Understanding Differentiation

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Understanding Differentiation

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

4.9+

13 M

#1

950 K+

Still not sure? Look at what your fellow peers are saying...

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

The application is very simple and well designed. So far I have found what I was looking for :D

Love this App ❤️, I use it basically all the time whenever I'm studying