How do I differentiate f(x) = a^x
The answer xa^(x-1) is not sufficient.
I think I'm supposed to substitute with e somehow to figure it out, but I'm not entirely sure how e works.
Can someone help me out? Please explain with detail.
How do I differentiate f(x) = a^x
The answer xa^(x-1) is not sufficient.
I think I'm supposed to substitute with e somehow to figure it out, but I'm not entirely sure how e works.
Can someone help me out? Please explain with detail.
$\displaystyle y = a^x$
$\displaystyle \ln{y} = \ln{a^x}$
$\displaystyle \ln{y} = x \ln{a}$
$\displaystyle \frac{d}{dx} \left[\ln{y} = x \ln{a} \right]$
$\displaystyle \frac{y'}{y} = \ln{a}$
$\displaystyle y' = y \cdot \ln{a}$
$\displaystyle y' = a^x \cdot \ln{a}$