Method OF Differentiation formulas

Every formula JEE Advanced expects you to know for Method OF Differentiation, with the variables spelled out. Free, no sign-up. Read it before a mock, not during one.

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Formulas: 34
Subject: Mathematics
Exam: JEE Advanced
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Method OF Differentiation, every formula

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Derivative (definition)
$f^{'} (x) = h \to 0 lim \frac{f ( x + h ) - f ( x )}{h}$
Constant
$\frac{d}{d x} (c) = 0$
Power rule
$\frac{d}{d x} (x^{n}) = n x^{n - 1}$
Exponential
$\frac{d}{d x} (e^{x}) = e^{x}$
General exponential
$\frac{d}{d x} (a^{x}) = a^{x} ln a$
Logarithm
$\frac{d}{d x} (ln ∣ x ∣) = \frac{1}{x}$
Sum/difference rule
$(c_{1} f \pm c_{2} g)^{'} = c_{1} f^{'} \pm c_{2} g^{'}$
Product rule
$(f g)^{'} = f^{'} g + f g^{'}$
Quotient rule
$(\frac{f}{g})^{'} = \frac{f ^{'} g - f g ^{'}}{g ^{2}}$
Chain rule
$\frac{d y}{d x} = \frac{d y}{d t} \cdot \frac{d t}{d x}$
d/dx sin x
$\frac{d}{d x} (sin x) = cos x$
d/dx cos x
$\frac{d}{d x} (cos x) = - sin x$
d/dx tan x
$\frac{d}{d x} (tan x) = sec^{2} x$
d/dx cot x
$\frac{d}{d x} (cot x) = - csc^{2} x$
d/dx sec x
$\frac{d}{d x} (sec x) = sec x tan x$
d/dx cosec x
$\frac{d}{d x} (csc x) = - csc x cot x$
d/dx arcsin
$\frac{d}{d x} (sin^{- 1} x) = \frac{1}{1 - x ^{2}}$
d/dx arccos
$\frac{d}{d x} (cos^{- 1} x) = \frac{- 1}{1 - x ^{2}}$
d/dx arctan
$\frac{d}{d x} (tan^{- 1} x) = \frac{1}{1 + x ^{2}}$
d/dx arccot
$\frac{d}{d x} (cot^{- 1} x) = \frac{- 1}{1 + x ^{2}}$
d/dx arcsec
$\frac{d}{d x} (sec^{- 1} x) = \frac{1}{∣ x ∣ x ^{2} - 1}$
Log-derivative rule
$\frac{d}{d x} ln f (x) = \frac{f ^{'} ( x )}{f ( x )}$
Root of a function
$\frac{d}{d x} f (x) = \frac{f ^{'} ( x )}{2 f ( x )}$
Power of a function
$\frac{d}{d x} [f (x)]^{n} = n [f (x)]^{n - 1} f^{'} (x)$
Parametric derivative
$\frac{d y}{d x} = \frac{g ^{'} ( t )}{f ^{'} ( t )}$
x=f(t), y=g(t)
Implicit differentiation
$\frac{d y}{d x} = - \frac{\partial f / \partial x}{\partial f / \partial y}$
f(x,y)=0
Logarithmic differentiation
$y = f^{g} : ln y = g ln f, then differentiate$
Derivative of f(x)^{g(x)}
$y^{'} = y [g^{'} ln f + g \frac{f ^{'}}{f}]$
Higher-order derivative
$\frac{d ^{2} y}{d x ^{2}} = \frac{d}{d x} (\frac{d y}{d x})$
d/dx (ax+b)/(cx+d)
$\frac{d}{d x} \frac{a x + b}{c x + d} = \frac{a d - b c}{( c x + d ) ^{2}}$
Derivative of even is odd
$f even \Rightarrow f^{'} odd (and f^{'} (0) = 0)$
√(a²−x²) substitution
$x = a sin θ$
√(a²+x²) substitution
$x = a tan θ$
Infinite nested radical
$y = f (x) + f (x) + \dots \Rightarrow \frac{d y}{d x} = \frac{f ^{'} ( x )}{2 y - 1}$

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Method OF Differentiation formulas

Method OF Differentiation, every formula

Derivative (definition)

Constant

Power rule

Exponential

General exponential

Logarithm

Sum/difference rule

Product rule

Quotient rule

Chain rule

d/dx sin x

d/dx cos x

d/dx tan x

d/dx cot x

d/dx sec x

d/dx cosec x

d/dx arcsin

d/dx arccos

d/dx arctan

d/dx arccot

d/dx arcsec

Log-derivative rule

Root of a function

Power of a function

Parametric derivative

Implicit differentiation

Logarithmic differentiation

Derivative of f(x)^{g(x)}

Higher-order derivative

d/dx (ax+b)/(cx+d)

Derivative of even is odd

√(a²−x²) substitution

√(a²+x²) substitution

Infinite nested radical

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