rules in derivative. Whats the difference between the 10th and the 11th rule?

Question

rule 10

f(x) = b^g(x)
then
f ' (x) = b^g(x) x ln b x g ' (x)

rule 11
f(x) = e^g(x)
then f ' (x) = e^g(x) x g ' (x)

i just wanted to know wheter the variable b and the variable e have a reason why they are that way or b and e are just the same. because i have to answer this problem and i dont know which one to use :s.

Answer 1

"b" indicates an unknown variable.

"e", however, is a special number with a very definite value. The value is 2.7182818284590452354...

If you see a lowercase e in an equation, it is almost always referring to this number, and not to a variable.

e has the special property that ln(e) = 1, which is why the natural logarithm term doesn't appear in rule 11, but does appear in rule 10.

Answer 2

e is not just another variable, it's a special symbol like pi. e=2.72 (approximately).

The thing about e, is that ln(e) = 1, so that's the difference in the two formulas. You'll notice that rule 11 pretty much is just missing the ln(b) that's in rule 10 because of the fact that ln(e)=1.

So yeah, I'd say they are the same rule, but 11 is showing you a special case.