Sindh Board Maths Second year Mathematics Book Chapter 3 Differentiation

 Class 12TH Maths Chapter 3 Differentiation

The differential calculus which is the branch of mathematics developed by isaac newtoon this branch is concerned with the problems of finding the rate of change of function with respect to the variable on which its depends in this chapter you can practice the folloing topics.

• Derivative of a function
• Distinguish between independent and dependent variables
• corresponding change in dependent variables
• Explain the concept of rate of change
• cofficient of function
• theorems on differentiation
• Application of theorems
• chain rule
• Diffrentiation and inverse trignometric functions

EX 3.1

in the exercise 3.1 you can must be undertsand the concept of the average rate of change of the functions varies from a to b the question basically what is the average rate function The rate of change is the speed at which a dependent variable changes with respect to independent variable it is generally expressed in dependent variable in independent variable.

EX 3.2

in the exercise 3.2 you can find the derivatives of the functions the process of finding derivatives is called the defferentiation and to find the derivative.

EX 3.3

in the exercise 3.3 it is easy exercise to understand but main thing is to clear your concept so in this exercise you can learn about the theorms of defferentiation you can prove the diffrent theorms for differentiation the 1st property of theorm is stated that The derivative of a constant is zero where c is a constant in given condition the property two is that The derivatives of any constant product of a function is equal to the product of that constant in the property three the derivative of a sum or difference of two fuction is equal to the sum of their derivative The next and the main topic youc can practicse and clear your concept is application of theorms on differentiation and you can remember this the derivative of an even fuction is always an odd function and viceversa.

EX 3.4

in the exercise 3.4 you can find the derivatives of the following using chain rule the chain rule for differentiating composite function is called chain rule in this we take the derivative of the outer function and then multiply it with the inner function.  

          

EX 3.5

in this exercise you can learn following topics differentiation of exponential and logarithmic functions you can find the derivatives using the principle you can also find derivative of algebraic expression ivolving product and power.