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Let

y = a^{x}

for some $a \in R, a > 0$ .

By taking $\ln$ of both sides of $y = a^{x}$ , express $a^{x}$ in the form $e^{k x}$ for some $k \in R$ .
Hence, find a formula for $\frac{d y}{d x}$
The functions $f, g, h$ are defined by
$\begin{aligned} f (x) & = 2^{x} \\ g (x) & = \sqrt{3^{x}} \\ h (x) & = {(\frac{1}{4})}^{x} \end{aligned}$
find expressions for $f^{'} (x), g^{'} (x)$ and $h^{'} (x)$ .

The value of

f^{'} (1) + 2 \sqrt{3} g^{'} (1) + 2 h^{'} (1)

can be expressed in the form

\ln (n), n \in N

Give the value of $n$ .