Jul 18, 2020
Calculus Help
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Calculus Help
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Calculus I: Derivatives
(created to be used in conjunction with the Great Book of Derivatives)
Heyy
I’m selling my notes and study guides online so I’m not really sure how this works but anyways if y’all wanna check it out that’s cool. This is a study guide for MATH 113 AKA Calc 1. It covers limits, IVT, Sandwich Theorem, and has explained practice problems. https://studysoup.com/guide/2709486/mason-mat-113-midterm-fall-2018-ash-zawacki
Product Rule Proof
d/dx[f(x)g(x)]=f(x)g'(x)+g(x)f'(x)
d/dx[f(x)g(x)]=limx->0 (f(x+h)g(x+h)-f(x)g(x))/h Limit definition
d/dx[f(x)g(x)]=limx->0 (f(x+h)g(x+h) -f(x+h)g(x)+f(x+h)g(x) -f(x)g(x))/h  -Did nothing!! Right? ;)
d/dx[f(x)g(x)]=limx->0 (f(x+h)g(x+h)-f(x+h)g(x))/h + (f(x+h)g(x) -f(x)g(x))/h Seperate into two fractions
d/dx[f(x)g(x)]=limx->0 (f(x+h)(g(x+h)-g(x))/h)) + (g(x)(f(x+h)-f(x))/h) Pull out a common factor
d/dx[f(x)g(x)]=limx->0 f(x+h) limx->0 (g(x+h)-g(x))/h) + limx->0 g(x) limx->0 (f(x+h)-f(x))/h) Limit definition
d/dx[f(x)g(x)]=f(x)g'(x)+g(x)f'(x)