Найти производные данных функций:
а)
y =x² +2Lnx ;
y ' = (x² +2Lnx) ' = (x²) ' +( 2Lnx ) ' =2x²⁻¹
+2*(Lnx) ' =2x +2/x =2(x+1/x).
===
б)
y =(x² +1)cos²5x ; * * * (u*v) ' =u'*v+v'*u * * *
y ' = ( (x² +1)cos5x ) ' =(x² +1) ' *cos5x +(x² +1)*(cos5x) ' =(2x+0)*cos5x +
(x² +1)*(-sin5x)*(5x) ' = 2xcos5x - 5(x² +1)*sin5x .
====
в)
y = x /√(3-x²) ;
y ' = ( x /√(3-x²) ) ' = (x*(3-x²)^(-1/2) ) ' =
(x) '*(3-x²)^(-1/2) +x *(-1/2)*(3-x²)^(-3/2)*(3-x²)' =1/√(3-x²) + x/√(3-x²)³ .
* * * иначе (3 - x² + x ) / (3-x²)√(3-x²) * * *