3. a) f'(x)=2x+4

b) f'(x)= 2x-(-1/x⁴)×x²'= 2x+2x/x⁴=2x+2/x³

c) f'(x)= -3x²/x⁶-(-4x³/x⁸)+(-5x⁴/x¹⁰)= -3/x⁴+4/x⁵-5/x⁶

d) f'(x)= 7×(rad de ordin 3 din x)⁶× (rad de ordin 3 din x)' = 7×(rad de ordin 3 din x)⁶×1/(3×rad de ordin 3 din x²)

e) f'(x)= 2x+e la x

f) f'(x)= 2la x ln2 + 5 la x ln5

g) f'(x)= 1/x -1

h) f'(x)= 2cosx-3sinx

i) f'(x)= 2x+2 la (-x) ln(-x)× (-x)'= 2x+2la (-x) lnx

j) f'(x)= 1/cos²x - 1/sin²x

4. a) f'(x)= 2x e la x+ x²×e la x=x e la x( 2+x)

b) f'(x)= [(x+1)'×x² - (x+1)×x²']/ x⁴= [x²-2x(x+1)]/x⁴= (x²-2x²-2x)/x⁴= (-x²-2x)/x⁴= (-x-2)/x³

c) f'(x) = [(x+3)'(x-2)-(x+3)(x-2)']/(x-2)'= (x-2 -x-3)/(x-2)²= -5/(x-2)²

d) f'(x) = [(x+1)'(x²+4)-(x+1)(x²+4)']/(x²+4)²= [x²+4-2x(x+1)]/(x²+4)²= (x²-2x²-2x+4)/(x²+4)²= (-x²-2x+4)/(x²+4)²

e) f'(x)= sin'x× cosx + sinx×cos'x= cosx×cosx+sinx×(-sinx)= cos²x-sin²x

f) f'(x)= x'×lnx+ x×lnx'= lnx+x×1/x= lnx +1