Question

Se considera functia f=x^2+2/x, calculati f'(x) ! Va rog ! 20p+coroana !

Answer 1

Răspuns:

Explicație pas cu pas:

$f(x)=x^2+\dfrac{2}{x} \\f '(x)=(x^2+\dfrac{2}{x} )'=(x^2)'+(\dfrac{2}{x} )'=2x+(2*\dfrac{1}{x} )'=2x+2*(\dfrac{1}{x} )'=2x+2*(x^{-1})'=2x+2*(-1)*x^{-1-1}=2x-2*x^{-2}=2x-2*\dfrac{1}{x^2}=\dfrac{2x^3-2}{x^2}=\dfrac{2(x^3-1)}{x^2}= \dfrac{2(x-1)(x^2+x+1)}{x^2}$