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se considera functia f:R→R , f(x)=2x^3+3x^2+5. aratati ca f'(x)=6x(x+1).x∈R

Răspuns :

f(x) = 2x³+3x²+5

f'(x) = 2•3x²+3•2x+0 = 6x²+6x = 6x(x+1)
[tex]f`(x)= (2x^{3} +3x^{2} +5)'=6x^2+6x+0=6x^2+6x=6x(x+1)[/tex], ∨ x∈ R