а)
y=2sinx - 4x
y' = 2cosx - 4
2*cos(π/3) - 4 = 2*1/2-4 = 1-4 = -3
б)
y = 1/3(tgx)
y' = 1/3(1/cos²x)
1/3*(1/cos²(-π/3)) = 1/3*(1/cos²(π/3)) = 1/3*4 = 4/3 = 1(1/3)
в)
y = -3cosx + x
y' = 3sinx + 1
3*sin(-π/6) + 1 = -3*sin(π/6) + 1 = -1,5 + 1 = -0,5
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Answers & Comments
а)
y=2sinx - 4x
y' = 2cosx - 4
2*cos(π/3) - 4 = 2*1/2-4 = 1-4 = -3
б)
y = 1/3(tgx)
y' = 1/3(1/cos²x)
1/3*(1/cos²(-π/3)) = 1/3*(1/cos²(π/3)) = 1/3*4 = 4/3 = 1(1/3)
в)
y = -3cosx + x
y' = 3sinx + 1
3*sin(-π/6) + 1 = -3*sin(π/6) + 1 = -1,5 + 1 = -0,5