Differentiate with respect to x: y=2^x

This question demonstrates how the exponential function can be used to simplify equations. In its current form the equation appears complex and the method is not clear. However, if we take the ln of both sides, we can simplfy this equation enormously: ln(y)=ln(2^x) Using the laws of logs we end up with the equation: ln(y)=xln(2). This can be differentiated easily via implicit differentiation to give: (1/y)(dy/dx)=ln(2). Multiplying by y gives: dy/dx=ln(2)y. The final step in this method is substituting our initial equation into this to give dy/dx=ln(2)2^x.
The reason this problem appears difficult is because taking ln of both sides is not an first obvious step. Furthermore, this method involves substituting an equation back into its derivative. Often this can throw people off as they do not initially calculate dy/dx in terms of x. The telltale sign of a problem like this is having a variable in a power.