А) у = e^(x²*Sinx)
y' = e^ (x²*Sinx) * (x²*Sinx)' = e^(x²*Sinx) * (2x*Sinx + x²*Cosx)
б) y = (x²*Cosx)/(x² - Sinx)
y' = ((x²*Cosx)' *(x² - Sinx) - (x²*Cosx)*(x² - Sinx)') / (x² - Sinx)² =
= (2x * Cosx - x² *Sinx) * (x² - Sinx) - (x² *Cosx)*(2x - Cosx) ) /(x² - Sinx)²
в) у = x^arcCos3x
y' =
г) у = ⁷√ ( (5х + 9)/(3х -1))⁸ = ( (5х + 9)/(3х -1))^8/7
у' = 8/7( (5х + 9)/(3х -1))^1/7 * ( (5х + 9)/(3х -1))' =
= 8/7* ⁷√(5х + 9)/(3х -1) * (5(3x -1) - 3(5x +9))/(3х -1)²=
= - 8/7* ⁷√(5х + 9)/(3х -1) * 32/(3х -1)²