Find the slope of the curve y=e^4x at x=0

Answer 1

If the equation is y = e^4x=(x)(e^4) then

dy/dx = d/dx(e^4(x)) = e^4 => the slope = e^4 for any value of x. It is a horizontal line of y = e^4

But if the equation is y = e^(4x) then

dy/dx = 4e^(4x). slope when x = 0 is 4(e^0) = 4 . It is still horizontal line at y = 4