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Differentiation: Rule If F (X) Then F' (X) Basic

This document provides rules and formulas for differentiation and integration. For differentiation, it lists the derivatives of basic functions like x^n as well as derivatives of more complex functions involving products, quotients, chains, logarithms, exponentials, and trigonometric functions. For integration, it lists integrals of basic functions, exponentials, trigonometric functions, and chains. It also discusses techniques like finding the area between two functions, using integrals to calculate displacement from velocity, and relationships between displacement, velocity, and acceleration.

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Jo-LieAng
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104 views2 pages

Differentiation: Rule If F (X) Then F' (X) Basic

This document provides rules and formulas for differentiation and integration. For differentiation, it lists the derivatives of basic functions like x^n as well as derivatives of more complex functions involving products, quotients, chains, logarithms, exponentials, and trigonometric functions. For integration, it lists integrals of basic functions, exponentials, trigonometric functions, and chains. It also discusses techniques like finding the area between two functions, using integrals to calculate displacement from velocity, and relationships between displacement, velocity, and acceleration.

Uploaded by

Jo-LieAng
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
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Differentiation

Rule If f(x) = Then f(x) =

Basic 1

Product () () ()() + ()()

() ()() ()()
Quotient
() (())2

(()) () ()
Chain
e.g. (()) ( ()) (())1

()
Logarithms ()
()

Exponentials () () ()

() () ()

Trig () ()()

() () 2 ()

Find tangent: Small changes:


first derivative, sub x-value, = + or
= |
( 1 ) = ( 1 ) =
Find normal: =
1
first derivative, sub x-value, = + or
1 e.g. find approx. change in y when
( 1 ) = ( 1 ) x changes from 2 to 2.03

Stationary point: () = 0
= | 0.03
=2
2
Second derivative: 2
2 Max stationary point: <0
2
2
Min stationary point: >0
2
Integration
Rule If () = Then () =

+1
Basic +
+1

Definite
integral
() () = () ()

1 +
Exponential + +

1
( + ) ( + ) +

Trig
1
( + ) ( + ) +

1 ( + )+1
Chain ( + ) +
+1
2
(() ())
1

Area between is
two functions

( )
1

Distance travelled: area under v(t) curve

If you have v(t), to find the displacement you integrate v(t) to s(t)

differentiate () integrate
()
differentiate integrate
()

s(t) displacement
v(t) velocity
a(t) acceleration If v(t) and a(t) have the same sign
increasing in speed
Initial: t=0
At origin: s(t) = 0 If v(t) and a(t) have opposite signs
Stationary or reverses: v(t) = 0 decreasing in speed
Constant or max/min velocity: a(t) = 0

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