finding limit using l'Hopitals rule

fran1942

Hello, I am tying to use l'Hopital's rule to solve this limit:
{e^(5+h)-e^5} / h
limit h tending towards 0

Using l'Hopitals rule I differentiate both numerator and denominator to get:
e^(5+h)-e^5 / 1
THen plugging 0 back in I get 0/1 which would give me a limit of 0 ?
But I think the limit should actually be e^5.

Can someone see where I have gone wrong ?
Thanks kindly

RoshanBBQ

What is the rate of change of e^5 with respect to h? I am assuming you are dealing with { e(5+h) - e^5 }/h.

fran1942

yes, that is correct. I am trying to apply l'Hopital's rule to that formula to obtain the limit as h tends towards 0.
I dont think I have it right in my attempt above. Any help would be appreciated.

Thank you.

Curious3141

e^5 is a constant. What's the derivative of a constant?