Find the first derivative of y=2^x

There is an initial subtle difficulty to this question, and it highlights understanding of the relationship between natural logarithms and the exponential function. One of the ways to solve this question, is to express y=2^x as y=e^(xln(2)), an entirely equivalent form. This is much easier to differentiate using the chain rule. The reason I chose this question is this is not the only way to find the derivative. If y=2^x ln(y)=ln(2^x) ln(y)=xln(2) differentiating implicitly dy/dx (1/y) = ln(2) rearranging dy/dx = yln(2) substitution of y=2^x dy/dx=ln(2)2^x I find this to be the most inspiring thing when explaining and learning mathematics, since there are so many different pathways to find the same answer, some with more elegance than others.