im supposed to diffrentiate 10^3x

i figured it was 3(10^(3x-1)) but apparently that is incorrect. why is that?

Printable View

- Sep 30th 2009, 03:41 AMfuror celticadifferentiation
im supposed to diffrentiate 10^3x

i figured it was 3(10^(3x-1)) but apparently that is incorrect. why is that? - Sep 30th 2009, 03:46 AMPlato
- Sep 30th 2009, 03:55 AMfuror celtica
i did not learn that formula! what happened to good ol' if f(x)= x^b then f'(x)=bx^(b-1)? can you show the proof to the formula that you used?

- Sep 30th 2009, 10:45 AMramiee2010
use formula

$\displaystyle \frac{d}{dx}(a^x) = a^x\ log \ a $

$\displaystyle \frac{d}{dx}(10^{3x}) = \frac{d}{dx}(1000^x) =1000^x\ log \ 1000 $

$\displaystyle \ =1000^x \ 3 \log10 =3\times 10^{3x}$