# definition of a derivative

• Oct 15th 2009, 09:23 AM
hazecraze
definition of a derivative
Find lim $(3^(2+h)^2)-81/h$.
h->0

*Should be 3 raised to the $(2+h)^2$, not (3) $(2+h)^2$*

How do I solve this? So f(x)= $3^(x^2)$, $f'= a^x =a^xlna$

I got: $f'(2)=3^(2^2)(ln3)$=81(ln3)
Key says: 324(ln3).
• Oct 15th 2009, 09:34 AM
Jester
Quote:

Originally Posted by hazecraze
Find lim $(3^(2+h)^2)-81/h$.
h->0

*Should be 3 raised to the $(2+h)^2$, not (3) $(2+h)^2$*

How do I solve this? So f(x)= $3^(x^2)$, $f'= a^x =a^xlna$
I got: $f'(2)=3^(2^2)(ln3)$=81(ln3)
Key says: 324(ln3).

Chain rule!

$f(x) = 3^{x^2}$ then $f'(x) = 3^{x^2} \ln 3 \cdot 2x$.