Chapter 2 - Derivatives - 2.3 Differentiation Formulas - 2.3 Exercises - Page 140: 19

$G'(q)=-2q^{-2}-2q^{-3}$

Make an «u» substitution in order to apply the chain rule and make it easier $G(u)=u^2$ $u=1+q^{-1}$ $u'=-q^{-2}$ Derivate $G'(u)=2u*u'$ Undo the substitution $G'(q)=2(1+q^{-1})(-q^{-2})$ $G'(q)=-2q^{-2}-q^{-3}$