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## Notes for week of 9/12/16

by: Brandon Short

12

1

2

# Notes for week of 9/12/16 Calculus 1151

Brandon Short
OSU

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These are just basic functions. I will bundle the notes we took in class in the future. That is why this is free.
COURSE
Math 1151 - Calculus 1 (11380)
PROF.
Professor Stephen Swihart
TYPE
Class Notes
PAGES
2
WORDS
KARMA
Free

## Popular in Calculus and Pre Calculus

This 2 page Class Notes was uploaded by Brandon Short on Sunday September 18, 2016. The Class Notes belongs to Calculus 1151 at Ohio State University taught by Professor Stephen Swihart in Fall 2016. Since its upload, it has received 12 views. For similar materials see Math 1151 - Calculus 1 (11380) in Calculus and Pre Calculus at Ohio State University.

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Date Created: 09/18/16
Overview week of 9/12/16 3.3 Rules of Differentiation Power of X:  d n (n­1) Power Rule:  /  Xdx= nX   Quotient Rule:  /  f(x)/g(x) = [(f(x) * g(x)) – (f(x) * g(x))] / [g(x)] 2 dx Product Rule:  /  [dxx) * g(x)] = [f(x) * g’(x)] + [g(x) * f’(x)] Chain Rule:  /  [dxg(x))] = [f(g(x))]’ * g’(x)  Constant Multiple: Power rule d /dx(cf(x)) = c * f ’(x) 3.4 Product and Quotient Rules Product Rule: While [f(x) +/­ g(x)]’ = f ‘(x) +/­ g’(x), The same does not apply to multiplication And division. [f(x)g(x)] ≠ f ‘(x) * g’(x) Instead: [f(x)g(x)] = [f(x) * g’(x)] + [g(x) * f’(x)] Products of multiple functions: (fg)’ = f’g + fg’ (fgh)’ = f’gh + fg’h + fgh’ (fghi)’ = f’ghi + fg’hi + fgh’i + fghi’ Quotient Rule: f(x) Finding ( / )’g(x)uotient Rule must be used.  Rule: f(x)’g(x) – f(x)g(x)’          g(x) 3.5 Derivatives of Trig Functions Memorize (sinx)’ = (cosx) (cosx)’ = (­sinx) (tanx)’ = (sec x) (cotx)’ = (­csc x) (secx)’ = (secx + tanx) (cscx)’ = ­(cscx)(cotx) Rule of thumb: f x with sinx or cosx is itself. (Not sure why he brought that up, but it may be  useful). Derivatives of certain terms (C)’ = 0 (x)’ = 1 n n­1 (x ) = n(x) (cf(x))’ = cf ’(x) (f(x) +/­ g(x)) = f ‘(x) +/­ g’(x) (e )’ = e  * k (e ) = e x

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