Explain why for any constant a, if y = a^x then dy/dx = a^x(ln(a))

So let's start with taking the natural log on both sides of y=a^x, giving us ln(y) = ln(a^x). Using the laws of logarithms we can write this as ln(y) = xln(a).Next, we differentiate both sides with respect to x, giving d/dx(ln(y)) = d/dx(xln(a)). As the term on the left hand side does not include any x terms we use the chain rule in order to differentiate with respect to y, dy/dx(d/dy(ln(y)) = d/dx(xln(a)) and then carry out the differentiation. We are then left with dy/dx(1/y) = ln(a), and, using some manipulation we find dy/dx = yln(a), and the original substitution leaves us with exactly what we're looking for y = a^x(ln(a)).