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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)/(1-cosx)

dy/dx = [(1-cosx)(sinx)-(1+cosx)(sinx)]/(1-cosx)^2 (quotient rule)

= [(sinx - sinx cosx) - (sinx + sinx cosx)]/(1-cosx)^2 (distribution)

= (-sinx cosx - sinx cosx)/(1-cosx)^2 (simplification)

= (-2sinx cosx)/(1-cosx)^2 (simplification)

Answer choices:

a. -1

b. -2 cscx

c. 2 cscx

d. (-2sinx)/(1-cosx)^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)]/[1-cos(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 Pre-Calculus, which was essentially a trigonometry class, so I had a particularly difficult time with this one)

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# Homework Help: Basic differentiation questions

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