Consider f ( x ) = x 3 + 4 x 2 − 1 {\displaystyle {}f(x)=x^{3}+4x^{2}-1} and g ( y ) = y 2 − y + 2 {\displaystyle {}g(y)=y^{2}-y+2} . Determine the derivative of the composite function h ( x ) = g ( f ( x ) ) {\displaystyle {}h(x)=g(f(x))} directly and by the chain rule.
