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f(x)=ln(1+1/x) calculează derivata functiei f

Răspuns :


[tex]\it \left(\ln\left(1+\dfrac{1}{x}\right)\right)' = \left(1+\dfrac{1}{x}\right)' \cdot \dfrac{1}{1+\dfrac{1}{x}} = -\dfrac{1}{x^2}\cdot\dfrac{x}{x+1}=-\dfrac{1}{x^2+x}[/tex]