definition of a derivative

**hazecraze** · October 15th 2009, 09:23 AM

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).

**Danny** · October 15th 2009, 09:34 AM

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

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