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# Harmony in Mathematics: Exploring Continuity and Differentiability for Class 12

Updated: Jun 17

Here's embarking on a journey to the fascinating world of Differential Calculus. Let's start with a question: Imagine you are driving a car and you want to know how fast you're going at a given instant. One of my student's Sarah answered the question. She said that you need to know the rate at which you are travelling at a given instant. So, basically that is the essence of Differential Calculus. So let's dive into Derivatives- the fundamental tool for calculating the rate of change. Derivatives is used in real life scenarios such as tracking the growth of population, modeling the motion of objects and understanding the behaviour of functions. As you dive into this page, you'll find yourself immersed in a world of mathematical elegance.

Find the value of the function at x =0 -CUET You'll solve problems that develop your analytical skills and appreciate the profound beauty of Differential Calculus. You'll develop the ability to solve particularly tricky questions that require a deeper understanding. Thus, the legacy of Differential Calculus continues inspiring you to embrace the power of mathematical thinking and explore the endless possibilities that lie ahead.

I am Suman Mathews, online math educator and tutor. Having taught Mathematics for three decades at high school and college, I can guide you through the journey of understanding Math and making it enjoyable in the process. If you follow my instructions, I can ensure that you score above 90 percent in your exams.

You'll learn how to study Continuity and Differentiation for Class 12 Mathematics, ISC and NCERT here. I am a math educator and online tutor teaching math for close to three decades. In this session, I'll be giving you useful tips on how to learn Differentiation.

## How important is Differentiation?

You need to keep in mind that Calculus for Class 12 Mathematics mainly comprises of Differentiation and Integration. Integration is basically the reverse of Differentiation. So, if you don't know Differentiation, you'll struggle with Integration.

## Continuity of Functions

You need to start with continuity of functions. That is, the basic definition of continuity in terms of limits. In this context, you will also learn about right hand limits and left hand limits for continuity.

Once you master problem solving in this, you will move on to the basic definition of derivative at a point. Learn about left hand and right hand derivative at a point. From here, you transition to the basic formulas on derivatives.

## Chain Rule and derivatives of Implicit functions

Once you get accustomed to the basic formulas of differentiation, you'll learn about the Chain Rule and it's applications. I teach my students a simple trick to use Chain Rule. You can sign up for my webinars on Differentiation, if you want to learn how.

You'll understand the basic difference between an Explicit and Implicit function. You derive an implicit function simply by differentiating both sides.

## Derivatives of Inverse Trigonometric Functions- Exponential and Logarithmic functions

You need to know inverse trigonometric functions at this stage. You can sign up for a webinar on Inverse Trigonometric Functions, if you want. You can also visit my page for free resources.

When you have to find the derivative of a function to the power of another function or in simple language, a complicated function, just apply log to both sides and differentiate. In this context, you'll need to learn basic derivatives of the log and exponential function, together with properties of the log function.

## Second Order Derivatives

Second order derivatives are quite simple actually, once you know first order differentiation. You simply have to differentiate twice. There are no additional formulas to remember.

Problems involving identities of second order derivatives are quite important and are generally asked in the board examinations of ISC, NCERT.

## Online webinars on Differentiation

Learn all this and more in my online webinars on Continuity and Differentiation. The entire topic may require around 8 to 10 classes. I will be covering formulas, concepts, MCQ questions, Assertion based questions, Case study questions and long answer questions in this webinar.

You aspire to do well in your mathematics exams. But, somehow, there are some concepts which you need help with. I can help you score above 90 percent or even a 100 in your Math exams, if you follow my instructions.

Having taught Mathematics for three decades at college and in high school, I know just what it is that you need to boost your score. I offer training for MCQ questions, logical and assertion based questions, case study based questions and other important questions.

## Group Classes

You will be regularly tested after completion of a chapter. So, join my roadmap. You can team up with four or five of your fellow students and have a group class in Differentiation.

Would you care to share this piece of information to others who may need it? Let's spread the word around, because "you are worth it". Math is meant to be easy, provided you get it right!

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