if y=2e^x+1, show that d^2y/dx^2 = y-1

Question

just a math question regarding exponential functions

Answer 1

y = 2e^x + 1

 

dy/dx = 2e^x

 

d²y/dx² = 2e^x = 2e^x + (1 - 1) = (2e^x + 1) - 1 = y - 1

 

Answer 2

I'm not sure how detailed you need this to be, but I will do my best to help you understand Arturo's answer.

For starters, I will assume you are clear that the notation d²Y / dX² means that you took the derivative twice. Of course, to do it twice, you first need to do it once:

Y = 2e^x + 1

Y' = 2e^x + 0        Because the derivative of e^u = e^u * u'    and constants derive to zero, always.

Y' = 2e^x

Now we get to do it again, whee!

Y" = 2e^x             Same as before, except we didn't have to derive that 1 on the end.

Now then: they told us that:

Y" = Y - 1           Let's plug in everything we know and check to see if that's true:

2e^x = 2e^x + 1 - 1

2e^x = 2e^x + 0

2e^x = 2e^x

I hope that helped clarify Arturo's reply for you.