Question

Segundo a regra de derivação, derive: x/(1+x^2)

Answer 1

f(x) = x / (1+x²)

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

f '(x) = 1 + x² - x [ 2x ] / 1+2x²+x⁴

f '(x) = 1+ x² - 2x² / 1+2x²+x⁴

f '(x) = 1-x² / 1+2x²+x⁴