In chapter 5, Continuity and Differentiability, we already learnt how to find a derivative of functions like composite functions, implicit functions, inverse trigonometric functions, logarithmic functions and exponential functions. In this chapter, we will learn about applications of derivatives in various fields, e.g., in social science, science, engineering etc. In this chapter, there are five exercises with 102 questions. The NCERT Solutions for Class 12 Maths Chapter6 Application of Derivatives are prepared by subject experts.
The derivative can be used to find equations of tangent and normal to curves, to determine the rate of change in quantities, to find turning points on the graph of the function, use the derivative to find approximate value of certain quantities and also use derivative to find intervals on which a function is increasing or decreasing. The five exercises of NCERT Class 12 Maths Chapter6 Application of Derivatives covers the rate of change of quantities, increasing and decreasing functions, approximations, tangents and normals and maxima and minima.
The derivative is the rate of change of distance(S) with respect to the time(t). In a similar manner, whenever one quantity (y) varies with another quantity (x), and also satisfy ,then or represents the rate of change of y with respect to x and or represents the rate of change of y with respect to x at . Let's take an example of a derivative
Example Find the rate of change of the area of a circle per second with respect to its radius r when r = 5 cm. Solution The area A of a circle with radius r is given by . Therefore, the rate of change of the area(A) with respect to its radius(r) is given by 
When Thus, the area of the circle is changing at the rate of 
6.1 Introduction
6.2 Rate of Change of Quantities
6.3 Increasing and Decreasing Functions
6.4 Tangents and Normals
6.5 Approximations
6.6 Maxima and Minima
6.6.1 Maximum and Minimum Values of a Function in a Closed Interval
NCERT Solutions for Class 12 Maths Chapter 6 Application of Derivatives Exercise 6.1
NCERT Solutions for Class 12 Maths Chapter 6 Application of Derivatives Exercise 6.2
NCERT Solutions for Class 12 Maths Chapter 6 Application of Derivatives Exercise 6.3
NCERT Solutions for Class 12 Maths Chapter 6 Application of Derivatives Exercise 6.4
NCERT Solutions for Class 12 Maths Chapter 6 Application of Derivatives Exercise 6.5
NCERT Solutions for Class 12 Maths Chapter 6 Application of Derivatives Miscellaneous
Chapter 1 

Chapter 2 

Chapter 3 

Chapter 4 

Chapter 5 

Chapter 7 

Chapter 8 

Chapter 9 

Chapter 10 

Chapter 11 

Chapter 12 

Chapter 13 
15) Find the equation of the tangent line to the curve which is (a) parallel to the line
4. Find the approximate change in the volume V of a cube of side x metres caused by increasing the side by 1%.
12) The radius of an air bubble is increasing at the rate of 1 /2 cm/s. At what rate is the volume of the bubble increasing when the radius is 1 cm?