definition of a derivative

Printable View

October 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).
October 15th 2009, 09:34 AM
Danny

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

All times are GMT -8. The time now is 08:58 AM.

Copyright © 2005-2013 Math Help Forum. All rights reserved.

Copyright © 2005-2013 Math Help Forum. All rights reserved.