#calculus study guide

[studyextraordinaire]

Calculus Help

[studyextraordinaire]

Calculus I: Derivatives

(created to be used in conjunction with the Great Book of Derivatives)

[dumbass-is-my-name]

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

[iisnotnormal-blog]

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)