For each function f(x) , find f'(x) f(x)=log(9) [2^(x)+1] The 9 is subscript Guys I am lost on this lonely road please help me.
Follow Math Help Forum on Facebook and Google+
change of base formula ... $\displaystyle \log_b(u) = \frac{\ln(u)}{\ln(b)} $ $\displaystyle \frac{d}{dx} \left[\frac{\ln(u)}{\ln(b)}\right] = \frac{1}{\ln(b)} \cdot \frac{u'}{u}$ this should be in your textbook.
so it would be d/dx [log(a) (f(x))] d/dx [ln(f(x))/ln(a)] f'(x) / f(x)ln(a) now im lost
is that right
$\displaystyle f(x) = \log_9(2^x + 1) $ $\displaystyle f'(x) = \frac{1}{\ln{9}} \cdot \frac{2^x \cdot \ln{2}}{2^x + 1}$
View Tag Cloud