Chain rule/R/x^2+5x-2 over x+1 and y-2 over y^2+3/Confirm/Exercise

Let

${}f(x)={\frac {x^{2}+5x-2}{x+1}}\,$

and

${}g(y)={\frac {y-2}{y^{2}+3}}\,.$

Determine the derivative of the composite

${}h(x)=g(f(x))\,$

directly and by the chain rule.

Create a solution