Calculus Essentials: Differentiation and Integration Guide, Summaries of Mathematics

Download Calculus Essentials: Differentiation and Integration Guide and more Summaries Mathematics in PDF only on Docsity!

Calculus-

• robhitz

Differentiation- (^) Integrations

Constants and Variables

• (^) > Constant Ygx-- variables^ ->^

· Variables - 1)

Independent (^) variables

1. (^) Dependent variables^ (y) > · 2y = 3n (^) + 4 Independent · · y

= Sinc

~ enque · y = 34 a y = 10gx · y

= x2+ 3x

1. Greatest^ integer functions W y = [x] [3.4] +>^3 [ & goo^ n^ =^30 =^ y =^ " y

= Sinn^ m = 45 =) y =

• y5z -^ n^ =^60 =)

n =^310 =)

y = 532

y =^ 3/

f(u) (^) = (^322) - 2x +

> & (2) + 2

= 3 =^2 + 1

f(- z) = 3(- 1)2 = 2(-

= G

f(z) -^ f(- 1) (^) = 2 - (^6) = -

change

• Differentiation y = f change^ #

-change

It is the ratio

of (^) change in (^) dependent variable

to

change in (^) independent voitable^ , when^ the -o change

in independent variable^ is

infinitesimally

small.

x, = 2

=

22 =^20000000000

00000000000

Diff (^) of

W.^ W.To x 00000005

• 22 - x) =^ AxD

# Derivative

of (^) y

. U.^ To x

=>^ Dx^ =^ 0X

y -^ x

·lg ast

in

a a

Find^ the^ derivative^ of^ following

1. Y

= 3 Sinn +

• logn

1. (^) Y

= tanx^ -^422 +^ 3x

I Geus

-^ -^ -

y = (^) (n3 +^ ( + 3 + 2 = All

• > (^17) Y =^3 Sinn^ +^ log ~ Product rule = (3 sinn +logn) Quotentsa

=d

sinn)

+logn^ v Chaina = (^3) Sinn +logn^ logsi y

dn

sinnz

an

= 3cm +

1

y = x+^ x

=+it a 12- = (^) 2x = (^) 2x

• • (^1)

= 2

• (^) Rules of differentiation

1. Addition and^ subtraction y = (^) utv y^ = =M^ dy = 3 + (^) (2) = 322 -^ 2x

outside to inside y = (^) logue =

y

logsinn

Sinn coa

y

loggintaz

an)

Sin(ntun) cos(2+^ an)^ (2x^

• (^) 4) = 22 +an)