RD Sharma Class 11 Solutions Chapter 30 - Derivatives (Ex 30.5) Exercise 30.5 - Free PDF
FAQs on RD Sharma Class 11 Solutions Chapter 30 - Derivatives (Ex 30.5) Exercise 30.5
1. What is Derivative according to the RD Sharma Class 11 Solutions Chapter 30 - Derivatives?
Derivatives of a Function represent the rate of change of the Function or a quantity concerning others.
Suppose there is a Function f is a real-valued Function. The Derivative of this Function at x can be defined as
\[\lim_{x\rightarrow 0}=\frac{f(x+h)-f(x)}{h}\]
This way of representing a Derivative is also called the first principle of Derivatives. Derivative of a Function can be denoted by a comma mark on top of the Function such as f’(x). Or we can write it as \[\frac{\mathrm{d} }{\mathrm{d} z}\]f(x).
2. What are the important topics and sub-topics covered in Chapter 30 - Derivatives in RD Sharma Class 11 Maths?
Chapter 30 - Derivatives is a very important Chapter as it is the basis of the calculus taught in Class 12. These are the most important topics covered in Class 6 Chapter 23 Limits -
Derivative at a point
A physical representation of Derivatives at a point.
Geometrical representation of Derivative at a given point
Derivative of a Function and its use as a rate measurer.
Differentiation from first principles of Derivatives
Differentiation from first principles.
Fundamental rules for differentiation (Product and Quotient rule)
Students will be able to easily grasp all these concepts by doing the Exercise questions given in the RD Sharma book.
3. What are the properties of Derivatives for given Functions as discussed in Chapter 30 - Derivatives?
If we assume f(x) = u and g(x) = v are two Functions defined in a common domain. Then the four properties of Derivatives for these equations are.
Derivative of the sum of two Functions is the same as the sum of Derivatives of those two Functions. i.e.
\[\frac{\mathrm{d} }{\mathrm{d} x}(u + v) = \frac{\mathrm{d} }{\mathrm{d} x}(u) + \frac{\mathrm{d} }{\mathrm{d} x}(v)\]
Same as addition, Derivative of difference of two Functions is the difference between the Derivatives of those two Functions
\[\frac{\mathrm{d} }{\mathrm{d} x}(u - v) = \frac{\mathrm{d} }{\mathrm{d} x}(u) - \frac{\mathrm{d} }{\mathrm{d} x}(v)\]
Product Rule: The product rule is used to find Derivatives of the product of two Functions. i.e.
(uv)’ = u’v + uv’
Quotient rule: This rule is used to calculate the Derivatives of the quotient of two Functions. i.e.
\[\left ( \frac{u}{v} \right )'=\frac{u'v-uv'}{v^{2}}\]
4. How many questions are there in Exercise 30.5 and what type of questions are there?
Chapter 30 - Derivatives cover five Exercises in total, each Exercise is very important for the upcoming Class 12. Exercise 30.5 is the last Exercise of this Chapter and it entails only 10 questions. These questions are based on all the concepts of the Derivatives discussed in earlier Exercises. This Exercise also targets the quotient rule of differentiation. The 10 questions in this Exercise are sufficient enough to make the students understand all these different concepts. Students can download the solutions to questions of this Exercise (Ex 30.5) from the website of Vedantu.
5. What are some real-life applications of the concept of Derivatives?
The concepts of Derivatives affect our real world in more ways than you might think, some applications of Derivatives are -
In big business, Derivatives are used to calculate the company’s profits and losses and changes in profits/losses by the use of Graphs.
Measurement of variations in temperature is done with the help of Differentiation.
To calculate speed and acceleration, Derivatives are a necessity.
They are also used to determine many quotations of Physics