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Basic differentiation questions 
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#1
Oct2108, 11:18 PM

P: 68

1. The problem statement, all variables and given/known data
Hello guys. I had to do some test corrections for my AP Calculus AB class. I have completed all of them besides the four below. Can anyone tell me where I go wrong? 1. Differentiate y = (1+cosx)/(1cosx) dy/dx = [(1cosx)(sinx)(1+cosx)(sinx)]/(1cosx)^2 (quotient rule) = [(sinx  sinx cosx)  (sinx + sinx cosx)]/(1cosx)^2 (distribution) = (sinx cosx  sinx cosx)/(1cosx)^2 (simplification) = (2sinx cosx)/(1cosx)^2 (simplification) Answer choices: a. 1 b. 2 cscx c. 2 cscx d. (2sinx)/(1cosx)^2 Choice D is the closest to my answer, however my answer multiplies cosx with the 2sinx. 2. Differentiate y = sin(x+y) I did this by implicit differentiation: y' = cos(x+y)[(x)+dy/dx] (doesn't seem correct...) Choices are: A. 0 b. [cos(x+y)]/[1cos(x+y)] c. cos(x+y) d. 1 9. Differentiate: y = (secx)^2 + (tanx)^2 y' = [(2secx)(secx tanx)] + [(2tanx)(secx)^2] (product rule) = 2 ((secx)^2)tanx + 2 tanx (secx)^2 = 2 (sec x)^2 + 3 tanx Choices are: a. 0 b. tan x + (secx)^4 c. ((secx)^2)((secx)^2 + (tan x)^2) d. 4 (secx)^2 tanx (I skipped PreCalculus, which was essentially a trigonometry class, so I had a particularly difficult time with this one) 


#2
Oct2208, 12:13 AM

P: 363

Hope that helps! 


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