Suppose I,J are intervals and a monotone onto f:I→J has an inverse g:J→I. Suppose you already know that both f and g are differentiable everywhere and f′ is never zero. Using chain rule but not Lemma 4.4.1, prove the formula g′(y)=f′(g(y))1. Remark: This exercise is the same as Exercise 4.1.10, no need to do it again if you have solved it already.