Derivative of $$$a^{u}$$$ with respect to $$$u$$$
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Your Input
Find $$$\frac{d}{du} \left(a^{u}\right)$$$.
Solution
Apply the exponential rule $$$\frac{d}{du} \left(n^{u}\right) = n^{u} \ln\left(n\right)$$$ with $$$n = a$$$:
$${\color{red}\left(\frac{d}{du} \left(a^{u}\right)\right)} = {\color{red}\left(a^{u} \ln\left(a\right)\right)}$$Thus, $$$\frac{d}{du} \left(a^{u}\right) = a^{u} \ln\left(a\right)$$$.
Answer
$$$\frac{d}{du} \left(a^{u}\right) = a^{u} \ln\left(a\right)$$$A