JEE Exam  >  JEE Notes  >  Differentiation for Physics

Differentiation for Physics - JEE PDF Download

What is a Function?

  • If the value of a quantity y (say) depends on the value of another quantity x, then y is the function of x i.e. y = f(x).
  • The quantity y is the dependent variable and the quantity x is the independent variable. For example, y = 2x2 + 4x + 7 is a function of x
    (i) When x = 1, y = 2(1)2 + 4x1+7 = 13
    (ii) When x = 2, y = 2(2)2 +4x2+7 = 23
  • As the value of y depends on the value of x, y is the function of x.

Differential coefficient or derivative of a function

  • Let y = f(x) …. (1)
    That is, the value of y depends upon the value of x.
  • Let ∆x be a small increment in x, so that ∆y is the corresponding small increment in y, then
    y + ∆y = f(x+∆x) …. (2)
  • Subtract (1) from (2), we get ∆y = f(x+∆x) − f(x)
  • Divide both sides by ∆x
    Differentiation for Physics - JEE
    Where Differentiation for Physics - JEE is called the average rate of change of y w.r.t. x.
  • Let ∆x be as small as possible i.e. ∆x→0 (read as delta x tends to zero)
  • Then, the differential coefficient or derivative of y w.r.t. x isDifferentiation for Physics - JEE

Theorems of Differentiations

  1. If y = C, when C is constant Differentiation for Physics - JEE
  2. If y = xn, where n is an integer Differentiation for Physics - JEE
  3. If y = Cu, where u is the function of x and C is constant Differentiation for Physics - JEE
  4. If y = u ± v ± ω ± ……, where u, v and ω are the function of x
    Differentiation for Physics - JEE
  5. If y = u v, where u and v are the function of x, then Differentiation for Physics - JEE
  6. If y =v/u, where u and v are the function of x, then Differentiation for Physics - JEE
  7. If y = un, where u is the function of x then Differentiation for Physics - JEE

Differential coefficients of Trigonometric Functions

Differentiation for Physics - JEE
Differentiation for Physics - JEE

Example: Differentiate the following w.r.t. x.

(i) sin 2 x
(ii) x sin x

(i) Let y = sin 2x
Differentiation for Physics - JEE

Differentiation for Physics - JEE

(ii) Let y = x sin x 

Differentiation for Physics - JEE


Differential Coefficients of Logarithmic and Exponential Functions

Differentiation for Physics - JEE
Differentiation for Physics - JEE
Differentiation for Physics - JEE

Example: Differentiate the follow w.r.t .x.

(i) 2 (logx)2
(ii) log(ax + b)

(i) Let y = (loge x)2

Differentiation for Physics - JEE

(ii) Let y  = log(ax + b)
Differentiation for Physics - JEE


Example: If S = 2t3 - 3t2 + 2,find the position, velocity and acceleration of a particle at the end of 2s. S is measured in metre and t in second

S = 2t3 - 3t2 + 2

When t = 2s, S = 2 × 8 – 3 × 4 + 2 = 6 m

Differentiation for Physics - JEE

The document Differentiation for Physics - JEE is a part of JEE category.
All you need of JEE at this link: JEE

FAQs on Differentiation for Physics - JEE

1. What is differentiation in physics?
Ans. Differentiation in physics refers to the mathematical operation used to determine the rate at which a physical quantity changes with respect to another quantity. It involves finding the derivative of a function, which represents the rate of change of the function at a particular point.
2. How is differentiation used in physics?
Ans. Differentiation is extensively used in physics to analyze the behavior and properties of physical quantities. It helps in understanding how variables such as position, velocity, and acceleration are related to each other. By differentiating equations, scientists can determine the rate of change of various quantities and study the dynamics of systems.
3. Can differentiation be used to analyze motion in physics?
Ans. Yes, differentiation plays a crucial role in analyzing motion in physics. By differentiating the equation of displacement with respect to time, we can obtain the equation for velocity. Similarly, differentiating the equation for velocity with respect to time gives the equation for acceleration. These derivatives help in understanding the motion of objects and their changing velocities.
4. What is the relationship between differentiation and kinematics?
Ans. Differentiation and kinematics are closely related in physics. Kinematics deals with the description of motion, whereas differentiation is used to analyze the changing rates of motion. By applying differentiation to kinematic equations, we can determine the relationships between position, velocity, and acceleration. This allows us to understand the behavior of objects in motion.
5. How does differentiation help in solving physics problems?
Ans. Differentiation helps in solving physics problems by providing a mathematical tool to analyze the changing rates of physical quantities. It allows us to determine the instantaneous rates of change, find relationships between different variables, and calculate important parameters like velocity and acceleration. By using differentiation techniques, scientists can model and predict the behavior of physical systems accurately.
Download as PDF
Explore Courses for JEE exam
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Download the FREE EduRev App
Track your progress, build streaks, highlight & save important lessons and more!
Related Searches

Extra Questions

,

Exam

,

Sample Paper

,

Differentiation for Physics - JEE

,

Important questions

,

mock tests for examination

,

Objective type Questions

,

practice quizzes

,

MCQs

,

pdf

,

Differentiation for Physics - JEE

,

Summary

,

shortcuts and tricks

,

Previous Year Questions with Solutions

,

past year papers

,

study material

,

video lectures

,

ppt

,

Semester Notes

,

Viva Questions

,

Differentiation for Physics - JEE

,

Free

;