Question

Sa se calculeze derivatele functiilor f:D→R:
a) f(x)= ln(1+sin²x), x∈R;
b) f(x)= sin(x$\sqrt{x}$), x∈(0,+∞)

Answer 1

sa ne amintim;

 (f(g))'= f'(g)* g'

atunci:
(ln (1+sin²x))'=

(1+sin²x)'/(1+sin²x)=2sinxcosx/(1+sin²x)=sin2x/(1+sin²x)

 si
(sin (x^3/2))'=cos (x^3/2) * ((x^(3/2))'= (3/2) x^(1/2) cos(x^(3/2)=
(3/2)*√x*cos (x√x)