A) f (x) = cosx, g (x) = 1/x2 + 1 b) f (x) = x2 + x - 1, g (x) = ctgx

Вычислим производные функций:

A) f (x) = cos x;

производная тригонометрической функции равна:

f ' (x) = (cos x) ' = - sin x;

c) g (x) = 1/x^2 + 1;

g ' (x) = (1/x^2 + 1) ' = (x^ (-2) + 1) ' = ((x^ (-2)) ' + 1 ' = - 2 * x^ (-2 - 1) + 0 = - 2/x^3;

b) f (x) = x^2 + x - 1;

f ' (x) = (x^2 + x - 1) ' = (x^2) ' + x ' - 1; = 2 * x + 1 + 0 = 2 * x + 1;

d) g (x) = ctg x;

g ' (x) = (ctg x) ' = - 1/sin^2 x.