Difference between revisions of "Calculus"

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====[[Calculus:Derivative of Polynomial Functions|Derivative of Polynomial Functions]]====
====[[Calculus:Derivative of Polynomial Functions|Derivative of Polynomial Functions]]====
#The sum rule in [[use Notation::Newton]] notation is <math>(f+g)'=f'+g'</math>
=======[[use Notation::Newton]] Derivative of Polynomial Functions=======
#The sum rule in [[use Notation:: Leibniz]] notation is <math>{d (f+g) \over d x} ={d f \over d x} + {d g \over d x}</math>
 
#The Difference Rule 1 <math>(f-g)'=f'-g'</math>
#The Difference Rule 2 <math>{d (f-g) \over d x}={d f \over d x} - {d g \over d x}</math>
 
#The Product Rule 1<math>(f*g)'=f*g'+ g*f'</math>
#The Product Rule 2<math>{d (f g) \over d x}'= f {d g \over d x} + g {d f \over d x}</math>
 
#The Quotient Rule 1<math>({f \over g})' = {(gf'-fg') \over g^2} </math>
 
#The Quotient Rule 2<math>{d ({f \over g})  \over d x} = {  g {d f \over d x} - f {d g \over d x} \over g^2} </math>
======[[use Notation::Newton]] Derivative of Polynomial Functions======
#The sum rule <math>(f+g)'=f'+g'</math>
#The sum rule <math>(f+g)'=f'+g'</math>
#The Difference Rule <math>(f-g)'=f'-g'</math>
#The Difference Rule <math>(f-g)'=f'-g'</math>
#The Product Rule <math>(f*g)'=f*g'+ g*f'</math>
#The Product Rule <math>(f*g)'=f*g'+ g*f'</math>
#The Quotient Rule <math>({f \over g})' = {(gf'-fg') \over g^2} </math>
#The Quotient Rule <math>({f \over g})' = {(gf'-fg') \over g^2} </math>
======[[use Notation::Leibniz]] Derivative of Polynomial Functions======
=======[[use Notation::Leibniz]] Derivative of Polynomial Functions=======
#The sum rule <math>{d (f+g) \over d x} ={d f \over d x} + {d g \over d x}</math>
#The sum rule <math>{d (f+g) \over d x} ={d f \over d x} + {d g \over d x}</math>
#The Difference Rule <math>{d (f-g) \over d x}={d f \over d x} - {d g \over d x}</math>
#The Difference Rule <math>{d (f-g) \over d x}={d f \over d x} - {d g \over d x}</math>
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#<math>(csc x)'= -csc(x) cot(x)</math>
#<math>(csc x)'= -csc(x) cot(x)</math>
#<math>(sec x)'= sec(x) tan(x)</math>
#<math>(sec x)'= sec(x) tan(x)</math>
====[[Calculus:Chain Rule|Chain Rule]]====  
====[[Calculus:Chain Rule|Chain Rule]]====
<math>[f(g(x))]'=f'(g(x))*g'(x)</math>
#[[use Notation::Newton]]Chain rule <math>[f(g(x))]'=f'(g(x))*g'(x)</math>


<math>\frac{d f(g(x))}{d x} = {{d f(g)} \over d g} {d g \over d x}</math>
#[[use Notation::Leibniz]]Chain rule <math>\frac{d f(g(x))}{d x} = {{d f(g)} \over d g} {d g \over d x}</math>


==Integration==
==Integration==

Revision as of 13:23, 25 July 2021

Calculus

This is a course that Henry and Ben are studying during 2021.

Differentiation

Limits

Power Rule

Derivative of Polynomial Functions

=Newton Derivative of Polynomial Functions=
  1. The sum rule
  2. The Difference Rule
  3. The Product Rule
  4. The Quotient Rule
=Leibniz Derivative of Polynomial Functions=
  1. The sum rule
  2. The Difference Rule
  3. The Product Rule
  4. The Quotient Rule

Derivative of Trigonometric Functions

Chain Rule

  1. NewtonChain rule
  1. LeibnizChain rule

Integration

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