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calculus exam 2 Cheat Sheet (DRAFT) by

MATH 1060 exam 2: sections 3.4-3.11, 4.1-4.4 Product and Quotient Rules, Trig limits and derivatives, IROC, Chain Rule, Implicit Differentiation, Deriv. of Logs, Exponentials, and Logarithmic Differentiation, Inverse Derivative, Inverse Trig, Related rates with trig functions, Basic max/min, f' undefined, RT, MVT, f', f'' graphs, graphing rational functions

This is a draft cheat sheet. It is a work in progress and is not finished yet.

Basic Proper­tie­s/F­orm­ula­s/R­ules

(fg)' = f' g + f g'
(f/g)' = (f' g - f g') / (g2)
d/dx(f­(g(x))) = f'(g(x­))g'(x)
d/dx(eg(x)) = g'(x)eg(x)
d/dx(l­ng(x)) = g'(x)/g(x)
d/dx(xn) = nxn-1
d/dx(c) = 0, c is any constant
bx = exlnb
 

Common Deriva­tives

Polyno­mials
d/dx(c) = 0
 
d/dx(x) = 1
 
d/dx(cx) = c
 
d/dx(xn) = nxn-1
 
d/dx(cxn) = ncxn-1
Trig Functions
d/dx(sinx) = cosx
 
d/dx(cosx) = -sinx
 
d/dx(tanx) = sec2x
 
d/dx(secx) = secxtanx
 
d/dx(cscx) = -cscxcotx
 
d/dx(cotx) = -csc2x
Inverse Trig Functions
d/dx(sin-1x) = 1/√1-x2
 
d/dx(cos-1x) = -1/√1-x2
 
d/dx(tan-1x) = 1/1+x2
 
d/dx(sec-1x) = 1/|x|√x2-1
 
d/dx(csc-1x) = -1/|x|√x2-1
 
d/dx(cot-1x) = -1/1+x2