Решение
1) y = sin⁶(10x)
y` = 6*10sin⁵(10x) = 60sin⁵(10x)
2) y = 2x arctg(e^x)
y` = 2*arctg(e^x) + (2x)* [1/(1 + e^2x)] * (e^x) =
= 2*arctg(e^x) + [(2x) * (e^x)] /(1 + (e^2x)]
3) y = [√(1 - x)/(1 + x)] - e^(x² + 2)
y` = 1 / [2√(1 - x)/(1 + x)] * [(-1 - x - 1 + x)/(1 + x)²] - 2x*e^(2 + x²)
- 1 / [(1 + x)² * √(1 - x)/(1 + x)] - 2x*e^(2 + x²)