im supposed to diffrentiate 10^3x i figured it was 3(10^(3x-1)) but apparently that is incorrect. why is that?
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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 $\displaystyle b>0~,~f(x)$ is a differentiable function and $\displaystyle y=b^{f(x)}$ then $\displaystyle y'=f'(x)b^{f(x)}ln(b)$.
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?
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 $ $\displaystyle \ =1000^x \ 3 \log10 =3\times 10^{3x}$
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