Question

Найти производная функции

1) $y=xcdot ln(x^{2}+1)+ln5$

2) $y = sinfrac{x}{2}cdot cosfrac{3x}{2}$

Answer 1

1) y' = (x*ln(x^2+1)+ln5)'=ln(x^2+1)+x(ln(x^2+1))'= ln(x^2+1)+(2x^2)/(x^2+1)

2) y'=(sin(x/2)*cos(3x/2))'=1/2cos(x/2)*cos(3x/2)-3/2sin(x/2)sin(3x/2)