Question

Seja f(x)=2x+3/x²+1 determine f'(x)

Answer 1

f(x)=2x+3/x^2+1
g(x)=x^2+1
h(x)=2x+3
g´(x)=2x
h´=(x)=2
f´(x)=g(x)*h´(x)-h(x)*g´(x)/[g(x)]^2
f´(x)=(x^2+1)*(2) - (2x+3)*(2x)/(x^2+1)^2
f´(x)=2x^2+2 - 4x^2 - 6x/(x^2+1)
f´(x)=-2x^2-6x+2/(x^2+1)^2