if y= e^(5x) what is dy/dx

For differentiation it is known that d/dx(e^x) = e^x always.This example is slightly more complex as it includes a product of x as the power.In this case we can simplify the question by setting 5x= u therefore y=e^u.Now we can differentiate this equation using the rule explained at the start and find dy/du=e^u.Then we must differentiate u with respect to x to find that du/dx= 5.looking back at the original question, what we are trying to find is dy/dx and what we have found so far is dy/du and du/dx.dy/dx can be found by multiplying the values for dy/du and du/dx as the du in the equations cancel, therefore it is equal to dy/dx. This gives dy/dx= 5e^u. If we sub back in u=5x then our final answer is, dy/dx=5e^5x