1. а)f(x) = 2Cosxtgx = 2Cosx*Sinx/Cosx = 2Sinx
f'(x) = 2Cosx
б) f(x) = (x² -6x +5)²
f'(x) = 2(x² -6x +5)*(2x -6)
2/ f(x) = Cos²x/4 - Sin²x/4 = Cosx/2
f'(x) = -Sinx/2 * (x/2)' = -1/2*Sinx/2
3. f(x) = (3x -5)³ + 1/(3 -x)²
f'(x) = 3(3x -5)² *3 - 2/(3 -x) *(3 -x)' = 9(3x -5) +2/(3 -x)
f'(2) = 9(9 -5) +2/(3 -2) = 36 +2 = 38
4. (f(g(x)))'=?
f(x) = x² -x, g(x) = 1/x
f(g(x)) = 1/x² - 1/x= (1 -x)/x²
(f(g(x)))' =( -1*x² - (1-x)*2x )/x⁴ =( -x² -2x +2x²)/х⁴ = (х² -2х)/х⁴ = (х -2)/х³
5. g(x) = tgx + tgπ = tgx
g'(x) = 1/Cos²x