1) y(x) = sin(5x) + 2^(3x-1)
y' = 5cos(5x) + 3*2^(3x-1)/ln2
2) y(x) = (4x + 1)^10
y' = 10 * 4(4x+1)^9 = 40(4x + 1)^9
3) y(x) = log2 (1-3x)
y' = -3 / [(1 - 3x) * ln(2)]
4) y(x) = arctg (x^2)
y' = 2x / (1 + x^4)
5) y(x) = ctg√x * ln(1/x)
y' = - ln(1/x) * / [2√x * sin²(√x)] - 1/x² * x * ctg√x = - ln(1/x) * / [2√x * sin²(√x)] - ctg√x / x