Y=2e^x Can someone explain how they get the answer so I'm not brain dead in class?

Question

jim_thompson5910 · Answer

What are the full instructions?

anonymous · Answer

To find the derivative

fibonaccichick666 · Answer

so, what is the derivative of e^x?

anonymous · Answer

I have no clue I missed that day of class because I was sick and he told me to get notes from a friend but the homework's due tomorrow

fibonaccichick666 · Answer

ok, well, lucky for you, the derivative of e^x is the easiest in existence :)

fibonaccichick666 · Answer

It is just, e^x.  It stays the same

anonymous · Answer

Really?

fibonaccichick666 · Answer

yup

fibonaccichick666 · Answer

it's special

anonymous · Answer

So does that mean by chance the derivative of this equation the same equation?

fibonaccichick666 · Answer

yep

jim_thompson5910 · Answer

yep that's how the number "e" is set up. It is its own derivative

if y = e^x, then dy/dx = e^x

anonymous · Answer

Thank you so much

fibonaccichick666 · Answer

we could prove it... but it is way easier to just take that as given

fibonaccichick666 · Answer

np, good choice of day to miss class

anonymous · Answer

So if any equation has e it's just the same equation as the derivative or are their special rules?

fibonaccichick666 · Answer

ah, so the chain rule comes into play if you have a function of x instead of just x as an exponent

anonymous · Answer

Oh okay thank you both so much

fibonaccichick666 · Answer

so, let's say you have $$e^{4x^2+2}$$
the derivative of f(x) which I will call u, is $$u'=8x$$ so then you need to derive $$e^u$$which equals$$e^u du=e^{4x^2+2}(8x)$$