Question

Fx= x^2-2x/3+x^2 найти производную

Answer 1

$\dfrac{2x^{2}+6x-6}{(3+x^{2})^{2}}$

Объяснение:

$f(x)=\dfrac{x^{2}-2x}{3+x^{2}};$

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

$=\dfrac{(2x-2) \cdot (3+x^{2})-(x^{2}-2x) \cdot 2x}{(3+x^{2})^{2}}=\dfrac{6x+2x^{3}-6-2x^{2}-2x^{3}+4x^{2}}{(3+x^{2})^{2}}=$

$=\dfrac{2x^{2}+6x-6}{(3+x^{2})^{2}};$