Question

4 задание. найти производную функцию

Answer 1

Решение
1)  y = 8x³ - 4/x - 7/x⁴ + x²/⁷
y` = 24x² + 4/x² + 28/x⁵ + (2/7x⁵/⁷
2)  y = ∛(x - 8)⁴ - 2/(1 + 3x - 4x²)
y` = (4/3)*∛(x - 8)  + 2*(3 - 8x)
3)  y = ctg³4x * arcsin√x
y` = [3ctg²4x * (- 1/sin²4x)* 4]*arcsin√x + ctg³4x * [1/√(1 - x) * 1/2√x]
4) y = (5x² + 4x - 2)(e^x)
y` = [(10x + 4) * (e^-x)  + (e^-x)*(5x² + 4x - 2)] / (e^x)²

Answer 2

2) y = ∛(x - 8)⁴ - 2/(1 + 3x - 4x²)
y` = (4/3)*∛(x - 8) + 2*(3 - 8x)//(1 + 3x - 4x²)²

Answer 3

4) y = (5x² + 4x - 2)(e^x)
y` = [(10x + 4) * (e^-x) + (e^-x)*(5x² + 4x - 2)] / (e^-x)²