# The Derivatives: Class 11 Mathematics Solutions | Exercise - 16.1

## Chapter - 16  The Derivatives

In this chapter, we are basically going to learn about the methods of finding derivative of a function, derivatives of algebraic, trigonometric, exponential and logarithmic functions by definition (simple forms) and by rules of differentiation.

So before moving towards the solution section, let us have a little concept about derivatives and the subtopics related to derivatives as well as some of the important formulas.

### Introduction

Differential calculus is a theory which has its origin in the solution of two old problems- one of drawing a tangent line to a curve and the other of calculating the velocity of non-uniform motion of a particle. In both the problems, the curves involved are continuous curves and the process used is the limiting process.

So the objects of study in the differential calculus are continuous functions. These problems were solved in a certain sense by Isaac Newton (English, 1642-1727) and Gottfried Willhelm Leibnitz (German, 1646-1716) and in the process differential calculus is discovered.

### Increment

A small change in the value of a variable is known as the increment. A change in the value of the variable may increase or decrease. But in either case, we use the term increment to denote the change. As for example, if the value of the variable changes from 2.0 to 2.0004 or from 2.0004 to 2.0 the change known as the increment is 0.0004.

Let y = f(x) be the function of x. If the value of x changes, the value of y will also change accordingly. Generally we denote by Δx (read as 'delta x') to change in x and Δy the corresponding change in y.

If x changes to x + Δx, y will change to y + Δy and f(x) changes to f(x + Δx) that is, f(x) = 2x + 3 then f(x + Δx) = 2(x + Δx) + 3

### Rules Of Differentiation

Here in this chapter, we'll learn about different rules of differentiation. We'll need these rules while solving the problems given in the exercises. So let's have a look at the different rules of differentiation.

• The sum rule
• The product rule
• The power rule
• The quotient rule
• The chain rule

### Exercise - 16.1

This PDF contains all the solutions of class 11, the derivatives Chapter. It only contains solutions of exercise - 16.1. If you want solutions of exercise - 16.2 and exercise -  16.3 then you'll find them above. You just need to click on the button given above.

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## Is Class 11 Mathematics Guide Helpful For Student ?

I have published this Notes for helping students who can't solve difficult maths problems. Student should not fully depend on this note for completing all the exercises. If you totally depend on this note and simply copy as it is then it may affect your study.

Student should also use their own will power and try to solve problems themselves. You can use this mathematics guide PDF as a reference. You should check all the answers before copying because all the answers may not be correct. There may be some minor mistakes in the note, please consider those mistakes.

## How to secure good marks in Mathematics ?

As, you may know I'm also a student. Being a student is not so easy. You have to study different subjects simultaneously. From my point of view most of the student are weak in mathematics. You can take me as an example, I am also weak in mathematics. I also face problems while solving mathematics questions .

If you want to secure good marks in mathematics then you should practise them everyday. You should once revise all the exercise which are already taught in class. When you are solving maths problems, start from easy questions that you know already. If you do so then you won't get bored.

Maths is not only about practising, especially in grade 11 you to have the basic concept of the problem. When you get the main concept of the problem then you can easily any problems in which similar concept are applied.

When your teacher tries to make the concept clear by giving examples then all students tries to remember the same example but you should never do that. You can create your own formula which you won't forget later.

If you give proper time for your practise with proper technique then you can definitely score a good marks in your examination.

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