1. Simplify the algebraic expression you get for Δy and Δy/Δx for the equation y=2^x 2. Use the difference quotient (f(x+h)-f(x))/h. No use of chain rule or other shortcuts. 3. I've tried a host of things, including raising terms to a natural log power (I.e. e^(ln2)*x*h), using logarithm properties, simplifying things... It seems that I cannot get rid of an h in some denominator. Now, this is a problem well before we actually learn derivatives, so things like that chain rule and implicit differentiation haven't been learned. This is a problem to challenge the kids with their difference quotient skills. I'm beginning to fear that it can't be done.