G(x)=3^x, write an expression for (g(x+h)-g(x))/ h

Another question I am having major trouble with. I have no idea how to do it. If you guys could help me, it would be much appreciated.

There are all kinds of equivalent expressions. I don't see that any of them are any better than the starting expression.
http://www.flickr.com/photos/dwread/5649…

What are your criteria for the form it should take?

g(x) = 3^x, so g(x + h) = 3^(x + h) = 3^x 3^h. So

[g(x + h) - g(x)]/h = [3^x 3^h - 3^x]/h

= 3^x(3^h - 1)/h.

This doesn't simplify further. (Though it can be shown that the term in parentheses tends to ln(3) as h -> 0.)

g(x) = 3^x
g(x+h) = 3^(x+h) = 3^x * 3^h

so g(x+h) - g(x) = 3^x * 3^h - 3^x = 3^x * (3^h-1)

so [g(x+h) - g(x)]/h = 3^x * [(3^h-1)/h]

This is wat i thnk

=(3^x + h - 3^x) / h
=h / h
=1