IIT JEE Test Series — Practice smarter, perform stronger.

Calculus AND Basic Maths formulas

Master Calculus AND Basic Maths through 24 JEE Advanced-level formulas, systematically structured with every variable spelled out. Revise concept-wise, identify the areas where you need improvement, and focus your preparation with greater precision.

Practise these formulas Know more about IIT JEE

Back to Formula Book

Calculus AND Basic Maths, every formula

24 formulas, typeset and free. Print it, or keep it open beside your practice.

Derivative of a power
$\frac{d}{d x} (x^{n}) = n x^{n - 1}$
Q1MCQPower rule
$\dfrac{d}{dx}(x^{4})$ equals:
- A
  $4x^{3}$
- B
  $x^{3}$
- C
  $4x^{4}$
- D
  $3x^{4}$
Derivative of a constant
$\frac{d}{d x} (c) = 0$
Derivative of sin/cos
$\frac{d}{d x} sin x = cos x, \frac{d}{d x} cos x = - sin x$
Q1MCQsin/cos
$\dfrac{d}{dx}(\cos x)$ equals:
- A
  $-\sin x$
- B
  $\sin x$
- C
  $\cos x$
- D
  $-\cos x$
Derivative of e^x and ln x
$\frac{d}{d x} e^{x} = e^{x}, \frac{d}{d x} ln x = \frac{1}{x}$
Q1MCQe^x, ln x
$\dfrac{d}{dx}(\ln x)$ equals:
- A
  $\dfrac1x$
- B
  $\ln x$
- C
  $x$
- D
  $e^{x}$
Product rule
$(uv)^{'} = u^{'} v + u v^{'}$
Q1MCQProduct rule
$(uv)'$ equals:
- A
  $u'v+uv'$
- B
  $u'v'$
- C
  $u'v-uv'$
- D
  $uv'$
Quotient rule
$(\frac{u}{v})^{'} = \frac{u ^{'} v - u v ^{'}}{v ^{2}}$
Q1MCQQuotient rule
$\left(\dfrac{u}{v}\right)'$ equals:
- A
  $\dfrac{u'v-uv'}{v^{2}}$
- B
  $\dfrac{u'v+uv'}{v^{2}}$
- C
  $\dfrac{u'}{v'}$
- D
  $u'v-uv'$
Chain rule
$\frac{d y}{d x} = \frac{d y}{d t} \cdot \frac{d t}{d x}$
Q1MCQChain rule
$\dfrac{d}{dx}\sin(x^{2})$ equals:
- A
  $2x\cos(x^{2})$
- B
  $\cos(x^{2})$
- C
  $2x\sin(x^{2})$
- D
  $\cos(2x)$
Integral of a power
$\int x^{n} d x = \frac{x ^{n + 1}}{n + 1} + C, n \neq = - 1$
Q1MCQPower integral
$\int x^{2}\,dx$ equals:
- A
  $\dfrac{x^{3}}{3}+C$
- B
  $2x+C$
- C
  $x^{3}+C$
- D
  $\dfrac{x^{2}}{2}+C$
Integral of 1/x
$\int \frac{d x}{x} = ln ∣ x ∣ + C$
Q1MCQ1/x integral
$\int\dfrac{dx}{x}$ equals:
- A
  $\ln|x|+C$
- B
  $-\dfrac{1}{x^{2}}+C$
- C
  $x+C$
- D
  $\ln x^{2}+C$
Integral of sin/cos
$\int sin x d x = - cos x + C, \int cos x d x = sin x + C$
Q1MCQsin integral
$\int\sin x\,dx$ equals:
- A
  $-\cos x+C$
- B
  $\cos x+C$
- C
  $-\sin x+C$
- D
  $\sin x+C$
Definite integral
$\int_{a}^{b} f (x) d x = F (b) - F (a)$
Slope as derivative
$slope = \frac{d y}{d x}$
Q1MCQSlope
The slope of a curve at a point is given by:
- A
  $\dfrac{dy}{dx}$
- B
  $\int y\,dx$
- C
  $\dfrac{d^{2}y}{dx^{2}}$
- D
  $y$
Area under a curve
$A = \int_{a}^{b} y d x$
Q1MCQArea
The area under a curve $y(x)$ from $a$ to $b$ is:
- A
  $\int_a^b y\,dx$
- B
  $\dfrac{dy}{dx}$
- C
  $y(b)-y(a)$
- D
  $\dfrac{y}{x}$
Maxima / minima condition
$\frac{d y}{d x} = 0$
Q1MCQExtremum
At a maximum or minimum, the derivative is:
- A
  $0$
- B
  $\infty$
- C
  $1$
- D
  undefined
Second-derivative test
$\frac{d ^{2} y}{d x ^{2}} < 0 (max), > 0 (min)$
Q1MCQSecond-derivative test
A point is a maximum if:
- A
  $\dfrac{d^{2}y}{dx^{2}}<0$
- B
  $\dfrac{d^{2}y}{dx^{2}}>0$
- C
  $\dfrac{d^{2}y}{dx^{2}}=0$
- D
  $\dfrac{dy}{dx}>0$
Small-angle approximation
$sin θ \approx θ, cos θ \approx 1, tan θ \approx θ$
Q1MCQSmall angle
For a small angle $\theta$ (in radians), $\sin\theta\approx$:
- A
  $\theta$
- B
  $1$
- C
  $0$
- D
  $\theta^{2}$
Binomial approximation
$(1 + x)^{n} \approx 1 + n x (∣ x ∣ ≪ 1)$
Q1MCQBinomial approx
For $|x|\ll1$, $(1+x)^{n}\approx$:
- A
  $1+nx$
- B
  $1+x^{n}$
- C
  $nx$
- D
  $1$
Average value of a function
$\overset{ˉ}{f} = \frac{1}{b - a} \int_{a}^{b} f d x$
Distance from velocity
$s = \int v d t$
Q1MCQDistance from v
The displacement from velocity is:
- A
  $\int v\,dt$
- B
  $\dfrac{dv}{dt}$
- C
  $vt^{2}$
- D
  $\dfrac{v}{t}$
Velocity from acceleration
$v = \int a d t$
Q1MCQVelocity from a
The velocity from acceleration is:
- A
  $\int a\,dt$
- B
  $\dfrac{da}{dt}$
- C
  $at^{2}$
- D
  $\dfrac{a}{t}$
Component of a vector
$A_{x} = A cos θ, A_{y} = A sin θ$
Q1MCQVector component
The x-component of a vector $A$ at angle $\theta$ is:
- A
  $A\cos\theta$
- B
  $A\sin\theta$
- C
  $A\tan\theta$
- D
  $A$
Magnitude of a vector
$∣ A ∣ = A_{x}^{2} + A_{y}^{2}$
Logarithm rules
$ln (ab) = ln a + ln b, ln a^{n} = n ln a$
Q1MCQLog rules
$\ln(ab)$ equals:
- A
  $\ln a+\ln b$
- B
  $\ln a\cdot\ln b$
- C
  $\ln a-\ln b$
- D
  $\dfrac{\ln a}{\ln b}$
Quadratic roots
$x = \frac{- b \pm b ^{2} - 4 a c}{2 a}$
Q1MCQQuadratic roots
The roots of $ax^{2}+bx+c=0$ are:
- A
  $\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$
- B
  $\dfrac{b\pm\sqrt{b^{2}-4ac}}{2a}$
- C
  $-\dfrac{b}{a}$
- D
  $\dfrac{-b}{2a}$

Other ways to revise this chapter

Master this chapter with similar other learning materials.

Preparing students for India’s top institutes

Our students are currently into top technological and medical institutes of India.

IIT Bombay
IIT Delhi
IIT Madras
IIT Kanpur
IIT Kharagpur
IIT Roorkee
IIT Guwahati
IIT BHU Varanasi
AIIMS Delhi
NIT Tiruchirappalli
NIT Rourkela
IIT Bombay
IIT Delhi
IIT Madras
IIT Kanpur
IIT Kharagpur
IIT Roorkee
IIT Guwahati
IIT BHU Varanasi
AIIMS Delhi
NIT Tiruchirappalli
NIT Rourkela

Join QuestPix, Today!

Get notified first, with exam & curriculum updates, course & test series launch offers, motivation & success stories and free learning resources recommended by toppers.

Calculus AND Basic Maths formulas

Calculus AND Basic Maths, every formula

Derivative of a power

Derivative of a constant

Derivative of sin/cos

Derivative of e^x and ln x

Product rule

Quotient rule

Chain rule

Integral of a power

Integral of 1/x

Integral of sin/cos

Definite integral

Slope as derivative

Area under a curve

Maxima / minima condition

Second-derivative test

Small-angle approximation

Binomial approximation

Average value of a function

Distance from velocity

Velocity from acceleration

Component of a vector

Magnitude of a vector

Logarithm rules

Quadratic roots

More JEE Advanced Physics formula sheets

Other ways to revise this chapter

Preparing students for India’s top institutes

Join QuestPix, Today!