Can you differentiate the following function using two methods:- y = e^(2x+1)

The first method to differentiate this fuction is the basic chain rule method. differentiate 2x+1 and add this to the front of the function. This gives us 2e^(2x+1). the other method to differentiate this function is by using logs. if you log both sides base of e (ln), you get ln(y) = 2x+1 and then differentiating both sides with respect to x gives (1/y)*dy/dx= 2. This when rearranged gives dy/dx = 2y and we know that y = e^(2x+1). We end up with the same solution as before.