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7. y = lntan(x/2), y' = [1/tan(x/2)] [sec(x/2)]^2 (1/2)
= (1/2) [cos(x/2)/sin(x/2)]/[cos(x/2)]^2 = 1/[2sin(x/2)cos(x/2)] = 1/sinx = cscx
8. y = [cos(x/2)]^5, y' = 5[cos(x/2)]^4[-sin(x/2)](1/2) = -(5/4)sinx[cos(x/2)]^3
11. y = x√(1-x^2) + arcsinx
y' = √(1-x^2) + x(-x)/√(1-x^2) + 1/√(1-x^2)
= √(1-x^2) + √(1-x^2) = 2 √(1-x^2)
7. y = lntan(x/2), y' = [1/tan(x/2)] [sec(x/2)]^2 (1/2)
= (1/2) [cos(x/2)/sin(x/2)]/[cos(x/2)]^2 = 1/[2sin(x/2)cos(x/2)] = 1/sinx = cscx
8. y = [cos(x/2)]^5, y' = 5[cos(x/2)]^4[-sin(x/2)](1/2) = -(5/4)sinx[cos(x/2)]^3
11. y = x√(1-x^2) + arcsinx
y' = √(1-x^2) + x(-x)/√(1-x^2) + 1/√(1-x^2)
= √(1-x^2) + √(1-x^2) = 2 √(1-x^2)
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