differentiation

**furor celtica** · September 30th 2009, 03:41 AM

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

**Plato** · September 30th 2009, 03:46 AM

Originally Posted by furor celtica

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

If $b>0~,~f(x)$ is a differentiable function and $y=b^{f(x)}$ then $y'=f'(x)b^{f(x)}ln(b)$ .

**furor celtica** · September 30th 2009, 03:55 AM

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?

**ramiee2010** · September 30th 2009, 10:45 AM

use formula
$\frac{d}{dx}(a^x) = a^x\ log \ a$
$\frac{d}{dx}(10^{3x}) = \frac{d}{dx}(1000^x) =1000^x\ log \ 1000$
$\ =1000^x \ 3 \log10 =3\times 10^{3x}$

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