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.

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- May 15th 2012, 02:20 PMTWNNeed help differentiating f(x) = a^x
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. - May 15th 2012, 02:38 PMPlatoRe: Need help differentiating f(x) = a^x
- May 15th 2012, 02:48 PMTWNRe: Need help differentiating f(x) = a^x
Can you explain in detail the process you underwent to reach that answer please?

- May 15th 2012, 03:26 PMskeeterRe: Need help differentiating f(x) = a^x
$\displaystyle y = a^x$

$\displaystyle \ln{y} = \ln{a^x}$

$\displaystyle \ln{y} = x \ln{a}$

$\displaystyle \frac{d}{dx} \left[\ln{y} = x \ln{a} \right]$

$\displaystyle \frac{y'}{y} = \ln{a}$

$\displaystyle y' = y \cdot \ln{a}$

$\displaystyle y' = a^x \cdot \ln{a}$