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Calculus Study Notes

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Handy calculus notes for prelim or hsc exams. The notes cover the aspects of the subject with step by step solutions and questions

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13 Pages Partial Study Notes > 2 Years old
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Calculus Study Notes
Topics this document covers:
Analytic geometry Differential calculus Rates Mathematical analysis Functions and mappings Derivative Slope Tangent Gradient Product rule Differentiation rules Expected value
This is a Partial Set of Study Notes

Partial Study Notes typically cover only single topics of a unit of study or do not cover multiple topics in significant detail. They are generally less than 20 pages in length.

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Topics this document covers:
Analytic geometry Differential calculus Rates Mathematical analysis Functions and mappings Derivative Slope Tangent Gradient Product rule Differentiation rules Expected value
Sample Text:
If we look at the results Function Derivative From the table we can develop a rule to differentiate 2xy = xy ′ = 2 nxy = 3xy = 3xy ′ = 2 nxy ′ = n 1- 4xy = 4xy ′ = 3 We can extend this to more complicated functions: xfy = )( n y = 1 x y ′ = - 1 x - 2 xnfy ′ = )( n - 1 × xf ′ )( = x - 1 Example 1: Differentiate the following: (a) xxy = 432 3 - + (b) y = - 52 x 4 + y ′ = 323 × x 2 - = 36 x 2 - = - 8 x 3 (c) (d) 4 2 (e) (f) y ′ = 24 -× x 3 xxy = 24 5 - - 3 xy = 62 - y ′ = 2 y ′ = 2345 × x 4 - -× x - 2 = 20 xx + 6 - xy = )53( - 6 xxy = )72( 2 - 5 y ′ = 3)53(6 x - 5 × y ′ = )74()72(5 xx 2 - 4 × x - = )53(18 x - 5 )72)(74(5 x ...
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