MA 161 Exam 2 study guide
MA 161 Exam 2 study guide MA 161
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This 4 page Study Guide was uploaded by Zack Bales on Wednesday March 2, 2016. The Study Guide belongs to MA 161 at Purdue University taught by Dr. Mummert in Spring 2016. Since its upload, it has received 158 views. For similar materials see Calculus I in Calculus and Pre Calculus at Purdue University.
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Date Created: 03/02/16
Calc 161 Exam 2 Study Guide Expression Derivative C 0 xp pxp-1 ex ex x x a Ln(a)a Ln(x) 1/x Cf(x) Cf’(x) f(x)+g(x) f’(x)+g’(x) f(x)-g(x) f’(x)-g’(x) f(x)/g(x) (f’(x)g(x)-g’(x)f(x))/ 2 (g(x)) f(x)*g(x) f’(x)g(x)+g’(x)f(x) f(g(x)) f’(g(x))g’(x) Sin x Cos x Cos x -sin x 2 Tan x Sec x Csc x -csc x cot x Sec x sec x tan x 2 Cot x -csc x -1 2 Sin x 1/sqrt(1-x ) Tan -1x 1/(x +1) Sinh x Cosh x Cosh x Sinh x Tanh x Sech x Sech x -sech x tan x Csch x -csch x coth x 2 Coth x -csch x Power Rule: d/dx (x ) = px-1 d/dx (C * f(x)) = C * d/dx (f(x)) Product Rule: d/dx (f(x)*g(x)) = f’(x)g(x)+g’(x)f(x) Quotient Rule: 2 d/dx (f(x)/g(x)) = (f’(x)g(x)-g’(x)f(x))/(g(x)) Trig Facts: Pi/6 Pi/4 Pi/3 Pi/2 Sin θ ½ 1/sqrt(2) Sqrt(3)/2 1 Cos θ Sqrt(3)/2 1/sqrt(2) ½ 0 Tan θ 1/sqrt(3) 1 Sqrt(3) DNE Tan x = sin x/cos x arcsin has domain [-1,1] range [- pi/2, pi/2] Sec x = 1/cos x arccos has domain [-1,1] range [0,pi] Csc x = 1/sin x arctan has domain (-Ꝏ,Ꝏ) range (-pi/2,pi/2) Cot x = cos x/sin x Cos x +sin x = 1 1+ tan x = sec x 2 Chain rule: d/dx(f(x)) = f’(x)(x’) Implicit Differentiation X +y = 1 d/dx (X +y ) = 0 2x+2yy’=0 2yy’ = -2x Y’ = -x/y Logarithmic Differentiation; d/dx (ln x) = 1/x d/dx (log a) = (1/ln a)(1/x) d/dx (ln 3x) = (1/3x)(3) = 1/x d/dx (ln 3 + ln x) = 0+1/x = 1/x d/dx (ln x ) = d/dx (2 ln x) = 2(1/x) = 2/x Hyperbolic functions: x -x Sinh x = (e – e )/2 x -x Cosh x = (e + e )/2 2 2 Cosh x – sinh x =1 Growth: Y’ = ky Y(t) = y eo kt t = (ln 2)/k t= time to double 2=e => double K = (ln 1/2 )/t => half life 1/2 Newton’s Law of Cooling dT/dt = k(T-T ) s Assume T is s0 if not given Related Rates: 1.Draw picture 2.Label things that change with variables 3.Identify equations 4.Differentiate using chain rule 5. Plug n chug
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