RD Sharma Class 12 Solutions Chapter 11 - Differentiation (Ex 11.7) Exercise 11.7 - Free PDF
FAQs on RD Sharma Class 12 Solutions Chapter 11 - Differentiation (Ex 11.7) Exercise 11.7
1. What is Differentiation?
A derivative of a function in terms of an independent variable is what Differentiation means in arithmetic. It is used to measure the function per unit change in the independent variable in mathematics. Anti-Differentiation is the total opposite of Differentiation.
With the use of Differentiation, we may find the rate of change of one quantity to another. It is advantageous in a lot of ways.
The following are some examples of real-life Differentiation:
Acceleration.
It aids in the calculation of tangent and normal to a curve.
It aids in calculating the highest and lowest points on a graph's curve.
2. What are Linear and Non - Linear functions?
Under Calculus, functions are often divided into two categories:
(i) Linear Functions
(ii) Non-Linear Functions
Through its domain, a linear function varies at a constant rate. As a result, the function's overall rate of change is the same as the rate of change at any given location.
Non-linear functions, on the other hand, have a rate of change that changes from point to point. The nature of variation is determined by the function's nature.
A derivative of a function is defined as the rate of change of that function at a given position.
3. What are the topics covered in the RD Sharma Class 12 solutions Chapter 11 - Differentiation?
The following are some of the main themes covered in this chapter's RD Sharma Solutions.
Recapitulation of the product rule, quotient rule and Differentiation of a constant with an illustration.
Differentiation of inverse trigonometric functions from first principles.
Differentiation of a function.
Differentiation of inverse trigonometric functions by the chain rule.
Differentiation by using trigonometric substitutions.
Differentiation of implicit functions.
Logarithmic Differentiation.
Differentiation of infinite series.
Differentiation of parametric functions.
Differentiation of a function with respect to another function.
Differentiation of determinants.
4. What are some generalizations in Differentiations?
Maps between infinite-dimensional vector spaces, such as Banach and Fréchet spaces, can also be defined as differentiable. Both the directional derivative, known as the Gateaux derivative and the differential, known as the Fréchet derivative, has a generalisation.
Many functions are not differentiable, which is a drawback of the classical derivative. However, a concept known as the weak derivative may be used to extend the concept of the derivative so that all continuous functions and many additional functions can be differentiated.
The concept is to embed continuous functions in a wider space known as the space of distributions, requiring simply that a function be differentiable "on average."
5. How to prepare for Chapter 11 - Differentiation?
Students need to be thorough with the foundation of the chapter, “Differentiation”. Students must have a strong base to build further on their knowledge and acquire more knowledge. It is imperative to students to learn concepts like Recapitulation of the product rule, quotient rule and Differentiation of a constant with an illustration, Differentiation of inverse trigonometric functions from first principles, Differentiation of a function, Differentiation of implicit functions, logarithmic Differentiation, Differentiation of infinite series. Students should also prepare by solving sample papers. Students can find free study materials at the Vedantu app and website.
