Server Error

Server Not Reachable.

This may be due to your internet connection or the nubtrek server is offline.

Thought-Process to Discover Knowledge

Welcome to nubtrek.

Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

Read in the blogs more about the unique learning experience at nubtrek.

User Guide

Welcome to nubtrek.

The content is presented in small-focused learning units to enable you to
think,
figure-out, &
learn.

Just keep tapping (or clicking) on the content to continue in the trail and learn.

User Guide

To make best use of nubtrek, understand what is available.

nubtrek is designed to explain mathematics and science for young readers. Every topic consists of four sections.

nub,

trek,

jogger,

exercise.

User Guide

nub is the simple explanation of the concept.

This captures the small-core of concept in simple-plain English. The objective is to make the learner to think about.

User Guide

trek is the step by step exploration of the concept.

Trekking is bit hard, requiring one to sweat and exert. The benefits of taking the steps are awesome. In the trek, concepts are explained with exploratory questions and your thinking process is honed step by step.

User Guide

jogger provides the complete mathematical definition of the concepts.

This captures the essence of learning and helps one to review at a later point. The reference is available in pdf document too. This is designed to be viewed in a smart-phone screen.

User Guide

exercise provides practice problems to become fluent in the concepts.

This part does not have much content as of now. Over time, when resources are available, this section will have curated and exam-prep focused questions to test your knowledge.

summary of this topic

### Algebra of Differentiation

Voice

Voice

Home

»  Understanding Algebra of Derivatives
how derivative applies to a function given as algebraic operations of several functions

→  product and division

→  function-of-function

→  parametric form of function

### Understanding Algebra of Derivatives

plain and simple summary

nub

plain and simple summary

nub

dummy

simple steps to build the foundation

trek

simple steps to build the foundation

trek

Support Nubtrek

You are learning the free content, however do shake hands with a coffee to show appreciation.
To stop this message from appearing, please choose an option and make a payment.

In this page, what is algebra of derivatives and conditions under which it is applicable are discussed.

Keep tapping on the content to continue learning.
Starting on "Understanding Algebra of Derivatives". In this page, what is algebra of derivatives and conditions under which it is applicable are discussed.

What does the title "Algebra of differentiation" or "Algebra of derivatives" mean?

• Properties to find derivatives of functions given as algebraic operations of several functions
• application of differentiation

The answer is "Properties to find derivatives of functions given as algebraic operations of several functions"

The mathematical operations are

•  addition and subtraction u(x) +- v(x)

•  multiple of a function a u(x)

•  multiplication and division u(x)v(x) and (u(x))/(v(x))

•  powers and roots [u(x)]^n and [u(x)]^(1/n)

•  composite form of functions v (u(x))

•  parametric form of functions v=f(r) ; u=g(r)

Given that f(x) = u(x)***v(x) where *** is one of the arithmetic or function operations.

Will there be any relationship between the derivative of the functions d/(dx) u(x) ; d/(dx) v(x) and the derivative of the result d/(dx) f(x)?

Algebra of differentiation analyses this and provides the required knowledge.

Note: In deriving the results, the functions are assumed to be continuous and differentiable at the points of interest. For specific functions at specific values of variables, one must check for the continuity and the differentiability before using the algebra of derivatives.

For example, consider
u(x) = x^2
v(x) = sin x
f(x) = x^2 sin x

From the standard results, it is known that
d/(dx) x^2 = 2x and
d/(dx) sin x = cos x.
What is d/(dx) x^2 sin x?

In this particular example multiplication is considered. Instead of multiplication, one of the arithmetic or function operations may be considered too.

The algebra of derivatives analyses this and provides the required knowledge.

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

Progress

Progress

What does the title : Algebra of differentiation, or, Algebra of derivatives mean.
find;given;algebraic;several
Properties to find derivatives of functions given as algebraic operations of several functions
application
application of differentiation
The answer is "Properties to find derivatives of functions given as algebraic operations of several functions"
The operations are, addition and subtraction; multiple of a function; multiplication and division ; powers and roots; composite form of functions ; parametric form of functions.
Given that f of x equals u of x star v of x. Where star is one of the arithmetic, or, function operations. Will there be any relationship between the derivative of the functions d by d x u of x ; d by d x v of x and the derivative of the result d by d x f of x? Algebra of differentiation analyses this and provides the required knowledge.
For example, consider u of x equals x squared, v of x equals sine x , f of x equals x squared sine x. From the standard results of derivatives, it is known that d / d x of x squared = 2 x and d by d x of sine x = cos x . What is d by d x of x squared sine x? In this particular example multiplication is considered. Instead of multiplication, one of the arithmetic or function operations may be considered too. The algebra of derivatives analyses this and provides the required knowledge.

we are not perfect yet...